1
NONMELT LASER ANNEALING OF BORON IMPLANTED SILICON
By
SUSAN K. EARLES
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2002
Copyright 2002
by
Susan K. Earles
This work is dedicated to Laurie and her friend, the English major.
ACKNOWLEDGMENTS
I would like to thank my research advisor, Dr. Mark E. Law, for his time and support
beginning in my senior year of undergraduate study and continuing throughout my entire
course of graduate study. Along with Dr Law, I have also been very fortunate to have
support throughout the years from Dr Gis Bosman and Dr Robert Fox. Their wonderful
personalities, character, and advice gave me the courage and desire to continue with my
graduate study here at the University of Florida. Dr Sheng S Li has also helped me keep
my sanity by enduring many of my technical questions and thoughts on various topics.
His advice, support, and encouragement have been very welcome over these last few
years. I must also thank Dr. Kevin S. Jones. His comments and advice have definitely
aided in providing direction to my research. Let me also acknowledge Dr Holloway for
stepping in at the last moment to serve on my committee. It has been a pleasure to have
the chance to talk with him after class and at various materials science events. I would
also like to extend a special thanks to Lauren, Edna, Mary, Erlinda, Jim, and Sharon (the
computer and administrative assistants) for all of their help and conversations over the
years.
I would like to thank the groups from Texas Instruments, Lucent, Intel, and Motorola
for making my intern experiences very enjoyable and sometimes educational. Each
internship was certainly unique. Mike, Peter, Craig, and Tim definitely made it
believable that even work can be entertaining. I also want to thank Gana Rimple and
Somit Talwar at Verdant for help with the laser anneals. Also, although they may be
iv
unaware of their positive influence, I am very grateful for and will always welcome
conversation and advice from Wolfgang Windl and Baylor Triplett. I also need to thank
the SRC and SEMATECH for the financial support provided for this work.
As for my friends and family, which I am very fortunate to have, I thank them for all
of their support. I thank Steve, Janet, Marty, Hernan, Jon, Doug, Lahir, Ibo, Dave,
Laurie, Michelle, Lesley, Hugo, Joe, Elaine, Heather, Ming-yeh, Meng, Sushil, Wish,
Aaron, Tony, and the rest of the former and current SWAMP group, for all of the lunch,
dinner, and phone conversations over the years. It is suddenly obvious why it took me so
long to finish up. So why stop now, I thank Lisa, Juan, and Derek for all of the much
needed babble breaks. I would like to let Patrick and my family members, Ester, Lester,
Beverly, Joe, Beulah, Ron, Angie, Tina, Teresa, Emily, Bob, Gail, Richard, Sandi, Ann,
Brent, Marissa, and Daniel, “Yes, it is time to buy a stove. I am actually done.”
v
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ................................................................................................. iv
LIST OF FIGURES ........................................................................................................... ix
ABSTRACT.......................................................................................................................xv
1 INTRODUCTION ............................................................................................................1
1.1 Motivation and Objective ......................................................................................... 1
1.2 Ion Implantation........................................................................................................ 2
1.2.1 Collisions and Damage ................................................................................... 3
1.2.2 Complications ................................................................................................. 4
1.3 Activation.................................................................................................................. 5
1.4 Annealing and Diffusion........................................................................................... 6
1.4.1 Overview......................................................................................................... 6
1.4.2 Rapid Thermal Annealing............................................................................... 8
1.4.3 Laser Annealing .............................................................................................. 9
1.5 Analysis Techniques ............................................................................................... 11
1.5.1 Chemical ....................................................................................................... 11
1.5.2 Electrical ....................................................................................................... 11
1.5.3 Structural....................................................................................................... 13
2 LASER ANNEALING ...................................................................................................20
2.1 Overview................................................................................................................. 20
2.2 Laser Beam Interaction with Silicon....................................................................... 20
2.3 The Temperature Model ......................................................................................... 21
2.4 Laser Interaction with Implanted Silicon................................................................ 23
2.4.1 Absorption Depth and Implant Energy ......................................................... 24
2.4.2 Silicon Interstitial and Boron Diffusion during Annealing........................... 24
2.4.3 Increasing the Number of Laser Pulses......................................................... 26
2.5 Determining the Melting Point ............................................................................... 27
2.5.1 The 308 nm Melting Point ............................................................................ 27
2.5.2 The 532 nm Melting Point ............................................................................ 28
3 EXPERIMENTAL INVESTIGATIONS OF THE EFFECTS OF NLA ON BORON
IMPLANTED SILICON: 308 NM EXCIMER LASER ...................................................38
vi
3.1 Overview................................................................................................................. 38
3.2 Experiments ............................................................................................................ 39
3.2.1 Increasing the Number of Laser Pulses: 308 nm Laser, 5 KeV Boron Implant
................................................................................................................................ 39
3.2.2 Increasing the Number of Pulses: 308 nm Laser, 1 KeV Boron Implant ..... 39
3.3 5 KeV Results and Discussion................................................................................ 39
3.4 1 KeV Results and Discussion................................................................................ 41
3.5 Concluding Remarks............................................................................................... 43
4 EXPERIMENTAL INVESTIGATIONS OF THE EFFECTS OF NLA ON BORON
IMPLANTED SILICON: 532 NM RUBY:YAG LASER.................................................50
4.1 Introduction............................................................................................................. 50
4.2 Increasing the Number of Pulses: 532 nm Laser, 500 eV Boron Implant ............. 50
4.2.1 Experiment .................................................................................................... 50
4.2.2 Results and Discussion.................................................................................. 51
4.3 Increasing the Number of Pulses: 532 nm Laser, 5 KeV Boron Implant ............... 52
4.3.1 Experiment ................................................................................................... 52
4.3.2 Results and Discussion................................................................................. 52
5 EFFECTS OF POST-PROCESSING AFTER NONMELT LASER ANNEALING.....61
5.1 Overview................................................................................................................. 61
5.2 High-Temperature Rapid Thermal Annealing after 308 nm NLA ......................... 61
5.2.1 Experimental Overview ................................................................................ 61
5.2.2 5 KeV Results ............................................................................................... 62
5.2.3 1 KeV Results .............................................................................................. 64
5.2.4 Discussion ..................................................................................................... 65
5.3 High-temperature rapid thermal anneals after 532nm NLA ................................... 66
5.3.1 Experimental Overview ............................................................................... 66
5.3.2 5 KeV Results and Discussion ..................................................................... 67
5.3.3 500 eV Results and Discussion.................................................................... 68
5.4 Furnace Anneals and Damage Evolution................................................................ 71
5.4.1 308nm NLA .................................................................................................. 71
5.4.2 532nm NLA .................................................................................................. 72
5.5 Conclusions............................................................................................................. 72
6 EFFECTS OF NLA ON MOBILITY AND ACTIVATION..........................................89
6.1 Introduction............................................................................................................. 89
6.2 Experimental Results .............................................................................................. 90
6.2.1 The 308 nm Experiments .............................................................................. 90
6.2.2 The 532 nm Experiments .............................................................................. 91
6.3 Discussion ............................................................................................................... 92
vii
6.3.1 Overview....................................................................................................... 92
6.3.2 Boron Activation, Deactivation, and Precipitation ....................................... 93
6.3.3 Boron Activation, Deactivation, Interstitials, and Diffusion ........................ 96
6.3.4 Mobility and Sheet Resistance..................................................................... 97
6.3.5 Mobility, Activation, and Loops ................................................................... 98
6.4 Conclusions........................................................................................................... 100
7 MODELING THE MOBILITY....................................................................................117
7.1 Introduction........................................................................................................... 117
7.2 Li’s and Linares’ Mobility Model......................................................................... 118
7.3 The Improved Mobility Model ............................................................................. 119
7.4 Conclusions........................................................................................................... 122
8 SUMMARY, CONCLUSIONS, AND FUTURE WORK ...........................................130
8.1 Summary ............................................................................................................... 130
8.2 Conclusions........................................................................................................... 132
8.3 Suggestions for Future Work ................................................................................ 133
APPENDIX
A TEMPERATURE SIMULATION DURING NLA USING FLOOPS........................135
B MODELING THE MOBILITY WITH FLOOPS........................................................153
LIST OF REFERENCES.................................................................................................158
BIOGRAPHICAL SKETCH ...........................................................................................162
viii
LIST OF FIGURES
Figure
page
1.1 Schematic of MOS transistor showing location of source drain extensions (SDE). .....15
1.2 Top plot shows the average diffusion length of a silicon interstitial after 1 ns and 10
ns. The bottom plot shows the diffusion lengths for boron after 1 ns and 10 ns for
intrinsic and transient enhanced (B-I Pair diffusion) diffusion. ................................16
1.3 The diffusion length of the silicon is divided by the diffusion length of the boron
interstitial pair and plotted versus temperature. This shows how much farther a
silicon interstitial can travel than a boron-interstitial pair at the same time and
temperature. ...............................................................................................................17
1.4 This plot shows how fast the surface cools after reaching a peak temperature of
1600K (1327oC). The top plot shows how long it takes to cool to room
temperature. The bottom plot shows how long it takes to cool to around 800oC. ....18
2.1 This plot shows the temperature versus time seen at various depths in the wafer
during the NLA. The top curve is the temperature at the surface of the wafer. The
bottom curve is the temperature at 100 Å into the wafer...........................................29
2.2 This figure shows the temperature distribution in the wafer during one 20ns pulse
with the 532 nm laser. It also shows the beginning of the cool down after the
pulse is turned off (time > 2.0x10-8s).........................................................................30
2.3 This plot shows the temperature versus time seen at the surface of the wafer when
the sample is irradiated with multiple pulses at a frequency of 100Hz. ....................31
2.4 These plots are magnified views of the plot in Figure 2.3. This shows a more
detailed view of how the temperature is distributed over depth during the 532nm
NLA. ..........................................................................................................................32
2.5 Illustration of the approximate amount of the 5 KeV boron implant which is
annealed during a 308 nm NLA. The entire area is annealed during a 532 nm
NLA. ..........................................................................................................................33
2.6 Sheet resistance vs laser energy density in 5 KeV, 1e15 B+/cm2 samples irradiated
with one 15 ns pulse using the 308 nm laser. ............................................................34
ix
2.7 Reflectivity versus laser energy density after one pulse with the 308 nm laser on 5
KeV, 2e15 B+/cm2 samples. ....................................................................................35
2.8 Sheet resistance versus laser energy density for the 5 KeV, 2e15 B+/cm2 samples
following one 20 ns pulse with the 532 nm laser.......................................................36
2.9 Reflectivity versus laser energy density for 5 KeV, 2e15 B+/cm2 samples annealed
with the 532 nm laser using a 20 ns pulse .................................................................37
3.1 SIMS of 5 KeV, 2e15 B+/cm2 samples as-implanted and after the NLA with 308 nm
laser, and after 1040oC,5 sec RTA.............................................................................44
3.2 Sheet resistance number of laser pulses for 5 KeV, 2e15 B+/cm2 samples following
an NLA with the 308 nm laser at 0.6 J/cm2. using a pulselength 15 ns and a
frequency of 10 Hz.....................................................................................................45
3.3 Plan-view TEM for 5 KeV, 2e15 B+/cm2 samples following one pulse (top left), 10
pulses (top right), 100 pulses (bottom right), and after a 1040oC, 5 sec RTA
(bottom right). For the NLA the 308 nm laser is used with a 15 ns pulse at a
frequency of 10 Hz and a laser energy density at 0.6 J/cm2. .....................................46
3.4 SIMS of the 1 KeV, 1e15 B+/cm2 samples as-implanted, after ten pulses, and after a
1040oC, 5 sec RTA. The 308 nm laser with a 15 ns pulse at 10 Hz is used. ...........47
3.5 Sheet resistance versus number of laser pulses for the 1 KeV, 1e15 B+/cm2 samples
using the 308 nm laser with a 15 ns pulse at 10Hz. The point at 0 pulses
represents the sample that just received the 1040oC, 5 sec RTA...............................48
3.6 Plan-view TEM of the 1 KeV, 1e15 B+/cm2 samples after 10 pulses using the 308
nm laser with a 15 ns pulse at 10Hz (left) and after the 1040oC, 5 sec RTA(right). .49
4.1 SIMS of the boron profiles as-implanted, following the NLA, and following the
1050oC spike anneal for the 500 eV, 1e15 B+/cm2 samples. ....................................54
4.2 Sheet resistance versus number of laser pulses for 500 eV, 1e15 B+/cm2 samples
annealed with the 532 nm laser at 0.35 J/cm2 using a 20 ns pulse. ..........................55
4.3 Plan-view TEM of the 500 eV, 1e15 B+/cm2 samples annealed with a 1050C spike
anneal. ........................................................................................................................56
4.4 SIMS of the boron profiles as-implanted, following the NLA, and following the
spike anneal for the 5 KeV, 2e15 B+/cm2 samples....................................................57
4.5 Plan-view TEM of the 5 KeV, 2e15 B+/cm2 samples annealed with the 532 nm laser
at 0.35 J/cm2 using one, 10, 100, and 1000 pulses at 100Hz and 20 ns/pulse. ........58
4.6 Sheet resistance versus number of laser pulses for 5 KeV, 2e15 B+/cm2 samples
annealed with the 532 nm laser at 0.35 J/cm2 using a 20 ns pulse. ..........................59
x
4.7
Sheet resistance versus junction depth comparing NLA and the conventional spike
anneal for a 500 eV and a 5 KeV boron implant. ......................................................60
5.1
SIMS profiles following NLA and 1000oC, 5sec RTA for 5 KeV are shown. 1e15
B+ ions/cm2 samples processed with the 308 nm laser. ............................................73
5.2
Sheet Resistance vs. Laser Energy Density following 1000oC, 5sec RTA for 5
KeV. 1e15 B+ ions/cm2 samples processed with the 308 nm laser. .........................74
5.3
TEM following 0.4 J/cm2 NLA, following 0.6 J/cm2 NLA, and following the RTA
(top pictures from left to right), and TEM of samples receiving 0.4, 0.5, or 0.6
J/cm2 NLA followed by RTA (bottom pictures from left to right)............................75
5.4
Percentage of loops extending to the surface versus laser energy density for
1000oC, 5sec RTA of 5 KeV. 1e15 B+ ions/cm2 samples processed with the 308
nm laser......................................................................................................................76
5.5
Defect density versus laser energy density for 1000oC, 5sec RTA of 5 KeV. 1e15
B+ ions/cm2 samples processed with the 308 nm laser. ............................................77
5.6
SIMS of 1 KeV, 1015 ions/cm2 B following 10 laser pulses, with 1040oC, 5 sec
RTA, and 10 pulse plus 1040oC, 5 sec RTA..............................................................78
5.7
Sheet resistance versus number of laser pulses for 1 KeV, 1015/cm2 B for samples
receiving just the NLA (NLA only) and those processed with 1040oC, 5 sec RTA
(with RTA).................................................................................................................79
5.8
Plan-view TEM of 1 KeV, 1e15/cm2 boron implanted silicon following (from left
to right) 10 shots, RTA only, 10 shots plus RTA. .....................................................80
5.9
SIMS of 5 KeV, 2e15 B+ ions/cm2 samples following NLA with the 532 nm laser
using a 20 ns pulse length at 100 Hz and 1050oC spike anneal compared with the
sample receiving just the spike anneal.......................................................................81
5.10 Sheet resistance versus number of laser pulses of 5 KeV, 2e15 B+ ions/cm2
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100
Hz and/or 1050oC spike anneal..................................................................................82
5.11 Plan-view TEM of 5 KeV, 2e15 B+ ions/cm2 samples following RTA alone, one
pulse plus RTA, and 10 pulses plus RTA. The NLA is at 0.35 J/cm2 with the 532
nm laser using a 20 ns pulse length at 100 Hz. The RTA is a 1050oC spike
anneal. ........................................................................................................................83
5.12 SIMS of 500 eV, 1e15 B+ ions/cm2 samples following NLA with the 532 nm laser
using a 20 ns pulse length at 100 Hz and 1050oC spike anneal compared with the
sample receiving just the spike anneal.......................................................................84
xi
5.13 Sheet resistance versus number of laser pulses of 500 eV, 1e15 B+ ions/cm2
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100
Hz and/or 1050oC spike anneal..................................................................................85
5.14 Plan-view TEM of the 500 eV, 1e15 B+/cm2 sample annealed with a 1050oC spike
anneal. ........................................................................................................................86
5.15 Plan-view TEM of 5 KeV, 1e15 B+ ions/cm2 samples after 750oC furnace anneal
(top left), NLA plus 750oC, 15 min furnace anneal (top right), NLA plus 750oC,
45 min furnace anneal (bottom left), and NLA plus 750oC, 90 min furnace anneal
(bottom right). The NLA is with the 308 nm laser using one 15 ns pulse at 0.6
J/cm2...........................................................................................................................87
5.16 Sheet resistance for the 5 KeV, 2e15/cm2 samples receiving the 532 nm NLA
and/or the 750oC furnace anneal. ...............................................................................88
6.1 The Hall mobility vs. laser energy density is shown following 1040oC, 5 sec RTA
for 5 KeV, 2e15 B+ ions/cm2 samples processed with the 308 nm laser. .................102
6.2
Plot of the percent activation vs. laser energy density following 1040oC, 5 sec RTA
for 5 KeV, 2e15 B+ ions/cm2 samples processed with the 308 nm laser. The
active dose measured with Hall effect is divided by the implanted dose of 2e15
ions/cm2 which is also the dose measured from SIMS. .............................................103
6.3
Mobility and active dose (hole density) versus number of laser pulses for 1 KeV,
1015/cm2 B for samples receiving just the NLA (NLA only) and those processed
with 1040oC, 5 sec RTA (with RTA).........................................................................104
6.4
Percent activation versus number of laser pulses for 1 KeV, 1015/cm2 B for
samples receiving just the NLA (NLA only) and those processed with 1040oC, 5
sec RTA (with RTA). Top picture represents the active dose divided by the dose
of the implant, 1e15 ions/cm2 and the bottom picture the active dose divided by
the dose determined from SIMS, 7.4e15 ions/cm2. ...................................................105
6.5
Mobility and hole density versus number of laser pulses of 5 KeV, 2e15 B+
ions/cm2 samples following NLA with the 532 nm laser using a 20 ns pulse length
at 100 Hz and/or 1050oC spike anneal.......................................................................106
6.6
Percent activation versus number of laser pulses of 5 KeV, 2e15 B+ ions/cm2
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100
Hz and/or 1050oC spike anneal. The active dose is divided by the dose of the
implant, 1e15 ions/cm2...............................................................................................107
6.7
Mobility and hole density versus number of laser pulses of 500 eV, 1e15 B+
ions/cm2 samples following NLA with the 532 nm laser using a 20 ns pulse length
at 100 Hz and/or 1050oC spike anneal.......................................................................108
xii
6.8
Percent activation versus number of laser pulses of 500 eV, 1e15 B+ ions/cm2
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100
Hz and/or 1050oC spike anneal. The top picture is for the active dose divided by
the dose of the implant, 1e15 ions/cm2, and the bottom picture is for the active
dose divided by the actual SIMS dose. ......................................................................109
6.9
Dose loss as a result of processing with the NLA and/or the RTA in the 500eV
samples processed with the 532 nm laser. The top plot shows the dose measure
from SIMS following each anneal step. The bottom plot shows the percent of
dose which is lost during the RTA.............................................................................110
6.10 Hole density and hole mobility versus sheet resistance measured using Hall effect.
As shown, the change in sheet resistance is not dominated by change s in
mobility, but by the hole density................................................................................111
6.11 Hole mobility versus loop density and interstitial density are plotted. No strong
trends exist over all of the data. .................................................................................112
6.12 Percent activation versus loop density and interstitial density. ...................................113
6.13 Hole mobility versus hole concentration for all processing conditions. The hole
concentration is determined by dividing the hole density by the junction depth
measured at a boron concentration of 1x1018/cm3. ....................................................114
6.14 Sheet resistance as a function of junction depth for all processes (top) and NLA
alone compared with the conventional RTA (bottom). XJ is measured at a boron
concentration of 1x1018/cm3. The arrows show the benefit of using NLA over
conventional processing anneals................................................................................115
6.15 Plots of the hole density and hole mobility are shown versus the average radius of
the loops. As you can see both plots show strong trends. As the average radius of
the loops increases, the hole density decreases and the hole mobility increases.......116
7.1 This plot compares the theoretical results to the experimental results for the hole
mobility versus number of laser pulses after 532 nm NLA. The 5 KeV, 2e15/cm2
samples are used. .......................................................................................................124
7.2 This plot compares the theoretical results with the experimental results for the hole
mobility versus number of laser pulses. The 1 KeV, 1e15/cm2 sample results
shown here are processed with the 308 nm laser.......................................................125
7.3 The hole mobility versus the number of laser pulses is shown for the 5 KeV,
2e15/cm2 samples processed with the 532nm laser. The simulation used here
included the dependence of the number of neutrals on the size of the loop. .............126
7.4 The sheet resistance versus the number of laser pulses is shown for the 5 KeV,
2e15/cm2 samples processed with the 532nm laser. The simulation used here
included the dependence of the number of neutrals on the size of the loop. .............127
xiii
7.5 The mobility versus the number of laser pulses is shown for the 1 KeV, 1e15/cm2
samples processed with the 308nm laser. The simulation used here included the
dependence of the number of neutrals on the size of the loop...................................128
7.6 The sheet resistance versus the number of laser pulses is shown for the 1 KeV,
1e15/cm2 samples processed with the 308nm laser. The simulation used here
included the dependence of the number of neutrals on the size of the loop. .............129
xiv
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
NONMELT LASER ANNEALING OF BORON IMPLANTED SILICON
By
Susan K. Earles
May 2002
Chair: Mark E. Law
Department: Electrical and Computer Engineering
A new method for creating heavily-doped, ultra-shallow junctions in boron-implanted
silicon will be presented. This method uses nonmelt laser annealing (NLA) to supply
energy to the surface region of the silicon at a ramp rate greater than 1010oC/sec. This
study concentrates on high-dose, non-amorphizing boron implants. Boron implants into
silicon at energies of 500 eV to 5 KeV at doses of 1e15 – 2e15 ions/cm2 are used.
Samples are analyzed using the following techniques: four-point probe (FPP), Hall
effect, secondary ion mass spectrometry (SIMS), and transmission electron microscopy
(TEM). The results from FPP and SIMS show increasing the number of laser shots
decreases the sheet resistance without increasing the junction depth. Hall effect
measurements show NLA can also increase the mobility. Also, NLA affects defect
nucleation. Following NLA numerous small defects are nucleated resulting in a dramatic
change in the defect population. This decrease in defect size and increase in population
are shown to increase the scattering in the layer which decreases the mobility. Using
xv
NLA, heavily-doped 20 nm p-type layers with sheet resistances around 600 Ohms/sq are
created. Also, NLA results in nearly 100% activation of the boron in the sample and
reduces the dose loss during post-processing.
To help understand the changes in defect populations and mobility measurements
introduced by the NLA, experiments as well as modeling efforts are made. A mobility
model implemented in FLOOPS (Florida’s Object Oriented Process Simulator) with
terms to account for these defects is presented. With this mobility model the sheet
resistance of the implanted layer as well as the mobility can be determined. Also, the
temperature distribution in the silicon during the NLA and the cool-down will be
implemented in FLOOPS. This temperature distribution along with the current process
simulation models allows the calculation of the defect population following the NLA to
be determined, thus allowing more accurate modeling during post anneals.
xvi
CHAPTER 1
INTRODUCTION
1.1 Motivation and Objective
Industry and individual consumer demand will always require electronic equipment to
offer more functions and ease of use while costing less, operating faster, and occupying
less space. When that electronic equipment contains integrated circuits (ICs), these
demands can often be met by shrinking the ICs. However, reducing the size of integrated
circuits relies on the ability to shrink feature sizes at all levels from the metal
interconnect lines down to the individual transistors. In the semiconductor industry, the
most common way to make these individual transistors is using the complementary
metal-oxide-semiconductor (CMOS) process using silicon [Jae93].
The CMOS transistors are considered n-type (NMOS) or p-type (PMOS) depending
on which carrier (electrons or holes) forms the channel in the device. One of the key
issues involved in scaling PMOS transistors is reducing the depth of the p-type
source/drain extensions (Figure 1.1). For example, junction depths less than 30 nm are
required for 70 nm gate lengths [Cur97]. The simplest method of producing p-type
junctions is to implant boron, a p-type dopant. After the implant, the wafer is typically
rapid thermally annealed (RTA) in an effort to activate the boron and remove damage
created by the implant. Ideally during the RTA the following events would occur: the
boron would stay in the region where it was implanted, each of the boron atoms would
occupy a substitutional site in the lattice resulting in 100% activation of the implanted
dopant, and the damage to the lattice created during the implant would be completely
1
2
removed. However upon annealing, the heating of the lattice and the damage from the
implant result in boron diffusion, boron clustering, and defect evolution [Cow90, Hof74,
Sol90]. This produces deeper junctions, lower boron activation, and reduced mobility.
Variations in the implant parameters and thermal annealing techniques are thus required
to produce shallower junctions.
Experiments show increasing the ramp-up rate during thermal processing has been
shown to decrease the transient enhanced diffusion (TED) of boron in silicon [Aga98,
Aga99, Dow99]. Plots of the ramp-up rate versus diffusion length show the ramp-up rate
would need to be around 1010 oC /sec to result in a diffusion length of zero, and hence no
TED [Cow96]. Unfortunately, conventional RTA systems have peak ramp-up rates of
200-400 oC. However, using a laser for thermal processing results in a ramp-up rate
which approaches the 1010 oC /sec that current data suggests is needed for zero TED. The
ramp-down or cooling rate is also dramatically higher for the laser-annealed sample since
only a small surface region of the wafer is heated during the nonmelt laser anneal (NLA).
Therefore, in an effort to reduce TED while achieving high dopant activation, the
following study investigates the effects of nonmelt laser annealing on silicon heavilydoped with boron.
1.2 Ion Implantation
Silicon requires the addition of impurities to improve its conductivity. When
impurities are intentionally added to silicon they are called dopants. Ion implantation is
the most practical technique available for introducing dopants into silicon. Ion
implantation is a process which is controllable and reproducible. Other methods which
introduce dopants via solid-source or gas diffusion are difficult to control and not as
reliable. These methods are also limited in the ability to only incorporate dopants up to
3
the solid solubility level. Ion implantation, however, allows dopants to be introduced into
the silicon at values above solid solubility.
1.2.1 Collisions and Damage
Essentially, during ion implantation a source of the desired dopant is vaporized and
then ionized. The ionized atoms can then be sorted via a mass analyzer. The desired
species can then be filtered out, producing a source of high purity ions for implantation.
Under a strong electric field, the desired ions can then be directed and accelerated into a
beam which can be aimed at the target which is the surface of the silicon wafer.
While the dopant atoms are being directed to the silicon surface, collisions between
atoms and electrons will occur, energy will be exchanged, and many dopant atoms will
lose energy and come to rest below the surface of the silicon. The ion can lose energy via
a combination of two processes: nuclear stopping or electronic stopping. For nuclear
stopping, the elastic scattering between the ion and nuclei of the solid is considered.
Electronic stopping is quite complicated. The inelastic scattering events must also be
considered since the ion interacts with the electrons in the crystal. This interaction can
cause ionization of the target (silicon) atoms, ionization of the implanted ion, and
excitation of valance and conduction band electrons.
These two stopping methods are used in calculations along with the implant energy to
determine the total distance the dopant ion travels into the silicon. The energy and angle
at which the dopant ions hit the surface determines how far the dopants reside below the
surface. The beam current and implant time determines how many dopant atoms will be
incorporated into the silicon. Typically the process designer is concerned with the
projected range, which is the average depth the dopant penetrates below the surface and
the projected straggle, which is the deviation from the projected depth. More detail on
4
the implantation process can be found in numerous books [Wol86, Sze88, Smi77],
dissertations [Bri01, Lil01, Liu96], and theses [Mil99, Liu94].
When the dopant collides with the silicon lattice, silicon atoms are often displaced,
increasing the number of silicon interstitials in the silicon lattice. Approximately 15 eV
is required to displace a silicon atom from its lattice site [Sze88]. Displaced atoms with
sufficient energy can then collide with other atoms causing them to be displaced. This
new interstitial profile is typically referred to as the damage profile. Aside from the dose
and energy of the implanted species, the damage profile is also affected by the mass of
the implanted species, the temperature of the silicon during implant, and the rate at which
the ions hit the silicon. For example, heavier, larger atoms and molecules such as
arsenic or BF2 implanted at a dose of 1e15 ion/cm2 and an energy of 5 KeV will create
more damage than boron atoms implanted at the same dose and energy. If the damage is
great enough, the silicon can be converted from crystalline to amorphous, which means it
lacks long-range order.
The amount of damage created will determine which type of defect evolves when the
wafer is heated. Jones et al. [Jon88] created a classification system for defects based on
the damage profiles from which they evolved. Type I extended defects form below
amorphization while Type II – IV require amorphization. Type V defects are considered
to occur when the implant dose approaches the solid solubility limit of the dopant in
silicon. Type V are generally considered to result in precipitates upon annealing.
1.2.2 Complications
Typically (100) silicon wafers are used in processing. For this surface, implanting
boron at an angle of zero degrees results in the most channeling. Often boron is
implanted at 7 degrees to minimize the channeling. However, there is much debate as to
5
whether implanting at an angle has any benefit for ultrashallow boron implantation. As
the implant energy is reduced the implantation process itself becomes more complex.
Lower implant energies are required to produce the shallower junctions. However, the
dopant must still have enough energy to penetrate the silicon. This limits the minimum
energy at which boron can be implanted. Also, during implantation surface sputtering
occurs. For deep profiles the majority of atoms sputtered off the surface are silicon
atoms. As the projected range of the dopant moves towards the surface and the surface
concentration of dopant increases, the atoms sputtered begin to become a mix of silicon
and the dopant. This results in a loss of dopants (dose-loss) and makes it more difficult to
predict the characteristics of the implanted layer
If the dose is high enough for a particular energy, the surface can become amorphized.
Amorphizing the surface prior to a laser anneal will cause complications as the
amorphized region will melt at a temperature around 200oC lower than crystalline silicon.
Also, when a region has become amorphized the effects of end-of-range (EOR) damage
developing during post-annealing must also be considered. For more information on ionimplantation the reader is encouraged to view Andreas Hossinger’s dissertation,
Simulation of Ion Implantation for ULSI Technology, at www.iue.tuwien.ac.at [Hos00].
1.3 Activation
During the post implantation anneal energy must be applied to the implanted region to
activate the boron. Activation typically involves substituting a boron atom for a silicon
atom in a lattice site. Silicon crystallizes in the diamond lattice structure, which has a
coordination number of 4. This means each of the silicon atoms is bonded to four
neighboring silicon atoms. When a p-type dopant (B, In, Al, or Ga) with three valence
electrons replaces one of the silicon atoms, it accepts another electron from crystal to
6
complete all four bonds. This produces a negatively charged ion and effectively results
in the donation of a hole to the valence band. This hole is now available to participate in
conduction. N-type dopants (P, As, and Sb), having five electrons available for bonding,
will similarly donate an electron to the conduction band when replacing a silicon atom.
Once substitutional, the energy needed to ionize the dopant being small (~a few
hundredth eVs) is easily supplied by lattice vibrations occurring at room temperature.
However, the energy needed to move the boron into a substitutional site (a few eVs)
typically requires an anneal step far above room temperature.
1.4 Annealing and Diffusion
1.4.1 Overview
Dopant activation, defect evolution, and dopant-defect interactions are all driven by
diffusion processes that occur during annealing. It is generally accepted that dopants
diffuse in silicon by interactions with interstitials, vacancies, or both. Boron is
considered to be a purely interstitial diffuser meaning it needs an interstitial to diffuse.
Many models have been created to predict the diffusion of various dopants in silicon
[Lil01, Gen99]. Many studies [Fai90, Cha96, Cow96, Sto97] have been performed to
show that during annealing, dopants, in the presence of damage such as excess
interstitials or vacancies, diffuse at rates which differ from the predicted equilibrium
values. For example, numerous studies show that boron in the presence of a high
concentration of interstitials will show increased diffusion or transient-enhanced
diffusion (TED) [Sto97, Pri99, Nap99, Nap00]. It is also believed that at high doses,
boron, in the presence of a high concentration of interstitials forms into immobile,
inactive or partially ionized clusters, or boron interstitial clusters (BICs) [Sto97, Col98a,
Col98b, Col00, Lil01]. Also, extended defects which evolve during the anneals are
7
believed to getter boron making it inactive. Increased diffusion and dopant deactivation
are both detrimental to obtaining an ultrashallow, highly doped layer. Thus, removal of
the excess interstitial population is essential.
The amount of damage removal and boron diffusion is determined by how much the
silicon interstitial and boron diffuse during the anneal step. The peak temperature and
time at peak temperature along with how fast the wafer is heated and cooled all add to the
thermal budget seen by the wafer. The diffusion length is calculated as
L = (Dt)1/2
(1.1)
where D is the diffusivity in cm2/s, and t is the time in seconds. The diffusivities used
were calculated using the expression:
D = D0 exp(Ea/kT)
(1.2)
where D0 is the exponential prefactor, Ea is the activation energy, k the Boltzmann’s
constant, and T the temperature. Using diffusivities generated by Florida’s Object
Oriented Process Simulator (FLOOPS), Figure 1.2 shows how the diffusion length of
silicon compares to that of boron over many different temperatures. The top plot shows
the diffusion length of the silicon interstitial after 1 ns and 10 ns at temperatures ranging
from 1200-1400oC. The bottom plot shows how far a boron atom can move in silicon
after 1 ns or 10 ns. The plot shows the intrinsic diffusion as well as the enhanced
diffusion which occurs when the boron pairs with an interstitial to diffuse. From these
figures it is shown that silicon diffuses remarkably faster than boron with the gap
between the diffusion lengths at a set time narrowing as the temperature is increased. To
further illustrate how much faster the silicon interstitial diffuses compared to the boron
interstitial pair, Figure 1.3 is presented. In this figure the diffusion length of the silicon
8
interstitial after 1 ns is divided by the diffusion length of the boron interstitial pair after 1
ns. At 1300oC, the silicon interstitial diffuses on average 1000 times farther than the
boron-interstitial pair.
1.4.2 Rapid Thermal Annealing
Rapid thermal annealing (RTA), also referred to as rapid thermal processing (RTP), is
the most popular technique used today to activate dopants following ion implantation.
The systems available process one wafer at a time. The system configurations can vary
greatly. However, for shallow junction formation, the goal is the same: rapidly heat the
wafer to a high temperature (900-1100oC) for a short time (a few seconds or less).
Lower temperatures for such short times result in little to no dopant activation and
insufficient damage removal. The time the wafer is held at peak temperature is often
referred to as the soak time. Ramp-up rates of 40-400oC are available [Aga99]. A
popular type of RTA is a spike anneal. This involves ramping the wafer up to peak
temperature and then ramping it down, holding it for only a few milliseconds at peak
temperature. The ramp-up rate and minimum hold time at peak temperature is limited by
the system configuration. Two common configurations are the lamp-based system and
the hot-walled system.
Since the process involves heating the whole wafer, the wafer is ramped up to 600700oC where it is held for a few seconds before ramping up to peak temperature. This
reduces the effects of stress that develops in the wafer due to thermal gradients and layers
with mismatched lattice constants. Unfortunately, the hold at 600-700oC increases the
thermal budget of the process. Also, since the whole wafer is heated, the whole wafer
has to cool down. The wafer cools by radiative cooling from the wafer surfaces and
conduction through the wafer holder. The lamp-based system has been shown to cool at
9
~70oC/sec and the hot-walled system at ~60oC/sec [Aga99, Aga98]. The slow cool-down
rates also add to the thermal budget seen by the wafer.
1.4.3 Laser Annealing
As previously mentioned, increasing the ramp-rate during RTA results in decreased
dopant diffusion [Aga99, Aga98, Dow99]. However, even the fastest available RTA
systems peak at a few hundred degrees Celsius per second. This prompts the need for an
anneal system with a faster ramp-rate. Laser annealing provides the fast ramping desired.
Laser annealing also offers faster cooling rates and reduces the thermal budget seen by
the wafer.
Laser annealing has also been referred to as laser thermal annealing (LTA) and laser
thermal processing (LTP). Many different types of lasers have been used. The YAG,
excimer, and C02 lasers are some of the more common ones. Studies of the effects of
laser radiation on solids date back to 1971 [Rea71]. Excimer laser annealing (ELA), for
example, uses an excited-dimer (excimer) laser for annealing.
During laser annealing a beam of photons is focused on a sample. Simply put, the
photons interact with the electrons in the sample which then transfer the energy to the
lattice. This causes localized heating in the area where the photons hit the sample. More
specifically, the wavelength of this light determines how the energy will be absorbed in
the silicon. The energy of the beam, or incident photon energy, is determined by the
equation:
E=hc/λ
(1.3)
with h equal to Planck’s constant, c equal to the speed of light, and λ equal to the
wavelength of the laser. With the bandgap of silicon around 1.12 eV laser energy greater
10
than this bandgap results in absorption via band-to-band transitions, which results in the
desired heating of the region. Since only a specific region of the material is heated the
wafer cools via surface radiation and thermal conduction. The high thermal conductivity
of silicon allows the region to cool from 1600K (1326oC) to room temperature in a few
tenths of a millisecond. This cooling rate can be calculated from Figure 1.4.
Previous studies have investigated the use of high power pulsed lasers to melt the
implanted layers to achieve high activation and abrupt junctions [Tsu99, Zha95].
Complications arising from melting and regrowth, however, limit the use of this
technique [Cho00, Pri00, Tsu99, Zha95]. When a region of the silicon is melted, a melt
front develops which increases the heated volume. Melted regions also recrystallize off
of the region which is not melted. Recrystallization off of an oxide, for example, would
result in polycrystalline material. To avoid the negative effects of melting the wafer, the
power of the laser can be reduced to produce heating without melting. This will be called
nonmelt laser annealing (NLA).
A typical sequence for the front end processing which leads up to the ultrashallow
junction anneal would be as follows:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Active area formation
N-well implant plus channel doping
Gate oxidation
Gate electrode fabrication
Gate reoxidation
Pre-amorphization implant
Dummy side-wall spacer formation
Source-drain implant
Side-wall spacer removal plus RTA
Extension implantation (ultrashallow layer)
Ultrashallow junction anneal (RTA or possibly a laser anneal)
11
Previous studies have investigated the use of high power pulsed lasers to melt the
implanted layers to achieve high activation and abrupt junctions [Tsu96, Tsu99, Zha95].
Complications arising from melting and regrowth, however, limit the use of this
technique [Cho00, Pri00, Zha95].
1.5 Analysis Techniques
1.5.1 Chemical
Secondary ion mass spectrometry (SIMS) is a destructive technique which can be used
to obtain a concentration versus depth profile of impurities in silicon. Typically, the
impurity of interest is the implanted dopant, which for this study is boron. During SIMS
a beam of ions is directed at the surface of the sample. When the beam hits the surface, it
causes atoms and molecules to be ejected, resulting in sputtering of the surface. These
ejected species are generally charged and hence termed secondary ions. These secondary
ions are then sent through a mass analyzer. A profile of the number of each species
detected at a particular mass is then obtained over the depth of sputtering. From this
profile the concentration versus depth profile of the impurity of interest is obtained.
As the implant energies are reduced and the layers more heavily doped the limitations
of SIMS begin to become apparent. Various debates exist over what part of the SIMS
profiles are real. Long tails in the profiles, which have been attributed to rough crater
bottoms, make it difficult to accurately determine junction depths and effective
diffusivities.
1.5.2 Electrical
To understand how the created layer can be used in a device, the electrical properties
of that layer must be known. The electrical properties are defined by the resistivity, the
carrier density, and the carrier mobility. The resistivity of the layer is dependent upon the
12
number of carriers present and the mobility of those carriers in that layer. For a single
type of carrier with a positive charge (a hole) resistivity is defined as
ρ = 1/qµn
(1.4)
where ρ is the resistivity, q is the charge of the carrier (1.602x10-19 C), µ is the carrier
mobility, and n is the density of free charges, or carrier density.
The four-point probe (FPP) is commonly used to measure the resistance of a layer.
The sheet resistance along with the thickness of the layer gives the resistivity. The fourpoint probe applies a current between two points to the surface and measures the resulting
voltage between the other two points. The tips of the probe are made of a very strong,
low resistivity metal and applied to the surface of the wafer with enough pressure to
effectively punch through any native surface oxide. To obtain the correct sheet
resistance, a correction factor based on the spacing of the probe tips and the sample
geometry must be applied as
R=
V
*F
I
(1.5)
where R is the sheet resistance, V is the measured voltage, I is the applied current, and F
is the correction factor.
The Hall effect is often used to measure the carrier density in the sample. Along with
the resistivity, knowing the carrier density allows the calculation of the carrier mobility.
The Hall effect is best explained with the use of Figure 1.5. Here, a current Ix and a
magnetic field Bz are applied. Assuming the sample is p-type then the carriers are holes
which have a positive charge. When the magnetic field is applied, the carriers, being free
and charged, are influenced by the magnetic field and deflected in the y direction. This
results in an accumulation of holes on one side of the sample and a depletion on the other.
13
This causes an electric field, EH, to be generated in the y-direction which increases until
it counteracts the effect of the applied magnetic field. Knowing the value of Ey, Bz , and
Ix along with the Lorentz force expression, the carrier density can be determined [Li93].
Thus, according to Equation 1.4, the carrier density and the resistivity can be used to
determine the Hall mobility. For p-type silicon at reasonably high concentrations
(>5x1019 ions/cm3), the Hall mobility measured does not equal the carrier mobility. To
determine the actual mobility the Hall mobility must be divided by the Hall factor.
Similarly, the carrier density found using Hall effect must be multiplied by the Hall factor
to obtain the actual carrier density. A detailed description of the Hall factor can be found
in many references [Li93, Li79, Lin81]. Essentially for low doping the Hall factor is
generally assumed to be one and therefore the results from the Hall effect are reasonable.
For heavier doping, the Hall factor drops below unity. The typical value used in
converting the data is 0.7. Therefore, for this work the Hall effect measurements are
converted using a Hall factor of 0.7.
1.5.3 Structural
Transmission electron microscopy (TEM) is a technique used to characterize the
defect structure. TEM is a destructive technique requiring a sample thin enough to allow
electrons to be transmitted through it. Sample preparation is slow and the resulting
sample is very delicate. Great care must be taken not to damage the sample throughout
the process. Detailed instructions on sample preparation can be found in earlier works
from University of Florida graduates [Liu96, Mil99]. Once the sample is thinned, the
sample is loaded into the vacuum chamber of the TEM. Basically, an electron beam is
focused on the thin region of the sample allowing some of the electrons to be transmitted
through the sample. This results in a directly transmitted beam and a diffracted beam.
14
Choosing a selected area of the diffraction pattern allows the user to obtain a dark-field
image of the sample which will typically have higher resolution than the bright-field
image. For plan-view imaging of the defects produced following anneals in implanted
silicon, the g220 condition is used with a magnification typically 50,000 to 100,000 times
the original size.
15
Poly
Gate
SDE
Gate Dielectric
EPITAXIAL LAYER
Lightly Doped Substrate
Figure 1.1 Schematic of MOS transistor showing location of source drain extensions
(SDE).
16
Root(Dt) of Interstitial (Å)
35
30
after 1ns
after 10ns
25
20
15
10
5
0
1150
1200
1250
1300
1350
1400
1450
Temperature (Celsius)
Root(Dt) of Boron (Å)
0.06
Intrinsic Diffusion after 1ns
B-I Enhanced Diffusion after 1ns
Intrinsic B Diffusion after 10ns
B-I Diffusion after 10ns
0.05
0.04
0.03
0.02
0.01
0
Figure 1.2 Top plot shows the average diffusion length of a silicon interstitial after 1 ns
and 10 ns. The bottom plot shows the diffusion lengths for boron after 1 ns and 10 ns for
intrinsic and transient enhanced (B-I Pair diffusion) diffusion.
17
1500
1000
I
Root(Dt) / Root(Dt)
B-I
2000
500
0
1150 1200 1250 1300 1350 1400 1450
Temperature (Celsius)
Figure 1.3 The diffusion length of the silicon is divided by the diffusion length of the
boron interstitial pair and plotted versus temperature. This shows how much farther a
silicon interstitial can travel than a boron-interstitial pair at the same time and
temperature.
18
Figure 1.4 This plot shows how fast the surface cools after reaching a peak temperature
of 1600K (1327oC). The top plot shows how long it takes to cool to room temperature.
The bottom plot shows how long it takes to cool to around 800oC.
19
Bz
++++++++
-------EH
d
L
Figure 1.5 Hall effect diagram.
I
CHAPTER 2
LASER ANNEALING
2.1 Overview
Understanding the effects of laser annealing on boron implanted silicon requires
knowing where the energy is deposited during the irradiation and how that energy affects
the silicon and boron in the lattice. Modeling the temperature distribution in the silicon
during the laser anneal will help aid in understanding these effects. In this chapter, a
model implemented in FLOOPS (Florida’s Object Oriented Process Simulator) will be
presented for the temperature distribution in the silicon during the laser anneal and during
the cooling of the wafer after and between laser pulses. Ideally the temperature
distribution versus depth could be used along with boron and defect models in FLOOPS
to predict the boron diffusion and defect distribution following the NLA. This of course
requires accurate modeling of the defect evolution and boron diffusion on nanosecond
time scales.
2.2 Laser Beam Interaction with Silicon
The light from a laser is highly directional. Using lenses, the light can be focused and
concentrated to a spot of any size. Unfortunately the light is also coherent which means
it is capable of self-interference. This scattering can cause the beam intensity to vary
across the irradiated leading to problems with uniformity. The lasers used in this study
have a variation in energy of only 3%. The 308 nm laser can irradiate a 5 x 5 mm2
sample during one pulse, and the 532 nm laser a 1 x 1 cm2 sample during one pulse over
the energy density ranges used in this work.
20
21
For the laser to interact with the silicon, it needs to transfer its energy to the lattice. It
can do this by accelerating particles in the crystal. When those particles collide with the
atoms in the lattice energy is transferred to the lattice via lattice vibrations, and heat is
created. Laser wavelengths in the UV range result in electromagnetic fields with high
frequencies. Since the atoms in the lattice are basically too heavy to respond
significantly to these fields the energy is transferred from the field to the lattice by the
electrons which, after being accelerated by the field, collide with the atoms in the lattice.
Thermal equilibrium of the carriers occurs in less than 10 ps [Woo81]. Of course the
bound electrons respond weakly to the field compared to the free electrons which are
easily accelerated by the field. The electrons that do not collide with the lattice re-radiate
or reflect the energy without adding heat to the lattice. In other words, the photons
generated by the laser are absorbed by the silicon through electron-hole excitations and
other absorption mechanisms which results in thermal equilibrium of the carriers in less
than 10 ps. For nanosecond pulses the plasma effects due to excited carriers are
negligible [Woo81].
2.3 The Temperature Model
Because the heating occurs so rapidly and the laser energy is highly directional, the
temperature gradients perpendicular to the surface are much greater than those parallel to
the surface. Therefore, the temperature can be modeled using the one dimensional heat
flow equation:
ρ ⋅ Cp ⋅ ∂ T/∂t = ∂/∂x(K ⋅ ∂T/∂x) + I0 ⋅ (1 - R) ⋅ α ⋅ e
-α ⋅ x
(2.1)
2
where Io is the intensity of the laser (W/cm ), R is the reflectivity, α the absorption
coefficient, x the depth in to the crystal (perpendicular to the surface), K is the thermal
22
3
conductivity, Cp is the heat capacity (J/goC), and ρ is the material density (g/cm ). The
variables ρ, Cp, K, α, and R are all temperature dependent. However, ρ is set to 2.33
g/cm3 for all simulations. To properly model the cooling of the wafer, the radiation of the
heat from the surface (x=0) and back-side (x=d) of the wafer is accounted for with the
following equation:
∂ T/∂tx=0,d = - (A ⋅ e ⋅ σ ⋅ T4 ) / (m ⋅ Cp)
(2.2)
where A is the surface area of the sample, e is the emissivity (0.4), and σ is the StefanBoltzmann constant (5.67e-12 W/cm2⋅K4), and m is the mass (ρ ⋅ sample volume).
These equations require knowledge of the absorption coefficient and reflectivity of the
boron implanted silicon at the lasers output wavelength as well as how it varies with
temperature. However, for these models the optical properties used are determined from
measurements made on crystalline silicon. Data for the boron-implanted silicon versus
temperature is not available. The following equations are analytical fits for the
temperature dependent optical properties:
Cp (T) = 24.236 + 2.344e-3 ⋅ T – 4.56e-5 ⋅ T2
(2.3)
K(T) = 90.065 ⋅ 1.0e-4 / (T-300.0)
(2.4)
α(T) = 2.26e-3 ⋅ exp(2.26e-3 ⋅ (T – 300.0))
(2.5)
R(T) = 0.382 + 4.0e-5 ⋅ (T – 300.0)
(2.6)
The optical properties of crystalline silicon can be found in many publications [Jel82,
Hil80, Zha96]. Using this model the temperature distribution in silicon can be estimated.
Similar results can also be obtained by setting the parameters to constant values. In this
case, Cp is set at 0.7 J/g-C, K at 1.6 W/cm-C, α at 125.0 cm-1, and R at 0.4. Figure 2.1
shows how the temperature varies over time at various depths for the 308 nm laser during
23
one 15 ns laser pulse at 0.6 J/cm2. Figure 2.2 shows how the temperature varies over
time at various depths for the 532 nm laser during one 20 ns laser pulse at 0.35 J/cm2.
Figure 2.3 shows the heating and cooling of the surface for 3 laser pulses at a frequency
of 100 Hz using the 532 nm laser at 0.35 J/cm2 with a pulse length of 20 ns. Figure 2.4
shows the magnified regions of the plot in Figure 2.3. A complete description of this
temperature model along with the FLOOPS files can be found in Appendix A.
2.4 Laser Interaction with Implanted Silicon
When the light in the UV range hits the silicon it interacts with the electrons and those
electrons collide with the atoms which transfers energy to the lattice and heats the crystal.
In a perfect crystal, the resulting temperature distribution would follow equation 2.1.
However, when the crystal has defects, those defects add to the number of electrons
which can affect the way the energy is distributed in the crystal.
To make Equation 2.1 more physically accurate the absorption coefficient, thermal
conductivity, and reflectivity must all be made dependent on the free carrier distribution
and the temperature of the silicon. Unfortunately, optical data does not yet exist for the
conditions needed. Optical measurements would need to be made on the silicon which is
heavily doped with boron during the laser anneal for optimum results.
Using Equation 2.1 gives a rough idea of how the temperature is distributed in the
silicon. Knowing that the laser radiation couples more with the loosely bound valence
electrons gives further insight into how the light will couple to ion implanted silicon.
After the implant the boron and the damage result in an increase in the number of loosely
bound electrons near the samples surface. This distribution of electrons should influence
how the energy is transferred and heat distributed during a single laser pulse. This would
mean that areas where the damage and boron is located could result in an increase in the
24
density in that region causing more of the energy to be deposited in that region. This
could theoretically decrease the absorption depth of the laser.
2.4.1 Absorption Depth and Implant Energy
How far the silicon interstitials can move is highly dependent on where the silicon
interstitials are in relation to the heating resulting from the absorption of the laser. The
absorption depth of the laser gives information on the maximum depth heated by the
laser. For example, if the implant damage is located deeper than where the energy is
absorbed, not much diffusion will occur. Take the following cases: A) a laser has an
absorption depth of 70 Å and the projected range of the implant is at 700 Å, B) a laser has
an absorption depth of 70 Å and the implant as a projected range of 20 Å. For case A, the
bulk of the damage which is near the projected range will not be affected by the laser
anneal. For case B, the bulk of the damage is at 20 Å which is within the region heated
by the laser. Figure 2.1 and 2.2 shows how the temperature varies versus time over
various depths. The lasers used in this work are a 308 nm excimer laser and a 532 nm
Ruby:YAG laser. The absorption depth for the 308 nm in crystalline silicon is around 70
Å. The absorption depth is around 8000 Å for the 532 nm laser. Picking implant
conditions which keep the bulk of the damage and the implant within the absorption
depth of the laser used will allow the entire implanted region to be annealed during the
NLA.
However, due to the way the temperature distributes in the wafer (Figures 2.1
and 2.2) the shallower implants will always see average temperatures higher than deeper
implants even when both are within the absorption depth of the laser.
2.4.2 Silicon Interstitial and Boron Diffusion during Annealing
As shown in Chapter 1, silicon interstitial diffusivity in silicon increases as the
temperature increases according to the following equation:
25
D = D0 ⋅ e
–Ea/k⋅T
(2.7)
Using Equation 2.7 it can be found that in 10 ns a silicon interstitial can diffuse 16 Å at
1200oC and 32 Å at 1400oC. This means that during a single 15 ns pulse interstitials can
begin to move to the surface or evolve into clusters. If the interstitials should start to
cluster, sub-microscopic interstitial clusters (SMICs), I2 defects, 311s, and loops could
form.
Boron also diffuses according to Equation 2.1. However, as shown in Figures 1.2 and
1.3, it can be shown that the boron-interstitial pair diffusion at 1200oC is around 1000
times slower than the silicon interstitial. This means that it would take around 1000 times
the number of laser pulses to move the boron the same distance as the silicon interstitials
move in one pulse. This also explains why it is possible to remove most of the implant
damage without causing significant boron diffusion when a high-temperature anneal is
applied to an implanted region for a short time.
When using the NLA technique, it is important to select the appropriate laser for the
NLA. For example, Figure 2.5 shows the boron profile after a 5 KeV, 2e15 ions/cm2
implant. It also shows the region which is heated during a 308 nm NLA. As shown, only
7% of the implanted layer is annealed during a 308 nm NLA where 100% is heated for a
532 nm NLA. This is because the absorption depth of the 308 nm laser is around 70 Å
while the 532 nm laser has an absorption depth between 5000 and 10000 Å. This means
that the 308 nm NLA is more effective for implant energies around 1 KeV or less and the
532 nm NLA for implant energies up to 5 KeV. In the following chapters, the implant
energy has been varied to show the effect of the laser’s absorption depth on the boron
diffusion and defect evolution.
26
2.4.3 Increasing the Number of Laser Pulses
Removing the damage after the implant requires annealing the implanted region. The
time and temperature that the damaged region sees will determine how much damage
remains in the crystal and how much the boron will diffuse. During one nonmelt 15 ns
laser pulse, there is time for the silicon interstitials to move around but perhaps not
enough time for all of the damage to be removed. To remove more damage it seems that
it would be ideal to increase the length of the laser pulse. Increasing the length of the
laser pulse however results in an increase in the temperature that the surface reaches.
According to the temperature model presented in Chapter 1, a 0.1 ms pulse at 0.6 J/cm2
would raise the surface to a temperature greater than the melting point of silicon
(~1410oC) most likely vaporizing the region. Of course, the temperature model in
Chapter one does not account for the phase change in the material that occurs at melting,
so calculating actual temperatures above the melting point of silicon is not reasonable.
Therefore, instead of increasing the length of the pulse, the damage can be removed
little by little by simply increasing the number of pulses. If the time between pulses is
long enough for the sample to cool back to room temperature, the surface temperature
should never exceed the temperature seen during the first pulse. Although the laser heats
just the surface during the pulse, the heat distributes through the bulk via thermal
conductivity. During subsequent pulses, if bulk heating occurs more boron or silicon
diffusion than that seen during the first pulse will occur due to the increase in temperature
over the region. Also, the initial temperature of the wafer determines the peak
temperature reached during the NLA with higher initial temperatures increasing the final
surface temperature. Bulk heating can be avoided by adjusting the pulse frequency of the
laser.
27
2.5 Determining the Melting Point
These initial experiments are designed to determine the melting point of the silicon
surface. To investigate the effects that nonmelt laser annealing has on boron diffusion
and defect evolution, experiments are performed which vary the laser energy density
during the NLA. Experiments are performed using both the 308 nm laser and the 532 nm
laser.
2.5.1 The 308 nm Melting Point
To ensure that the regions studied will not be melted, an initial set of experiments is
performed using the 308 nm laser. For this set of experiments, 0.5 by 0.5 cm2 silicon
samples each implanted with 1015 B+ ions/cm2 at 5 KeV are used. Each sample is
irradiated at a given energy density with one pulse. For the 308 nm laser, the laser
energy density is varied from 0.35 to 0.75 J/cm2 and the pulse length is 15 ns. During
each laser anneal, a HeNe laser is bounced off the surface of the sample to measure
reflectivity. The reflectivity plateaus when the surface melts. For these samples, the
plateau is at 0.7. After all of the samples are annealed the sheet resistance of each sample
is measured using a four-point probe. Plots of the sheet resistance versus laser energy
density along with the point when the surface reflectivity plateaus show the maximum
energy density which can be used to perform non-melt laser annealing.
The results for the sheet resistances versus laser energy density using the 308 nm laser
and for the reflectivity versus laser energy density are shown in Figures 2.6 and 2.7
respectively. As you can see in the figures, the crystalline silicon melts at around 0.62
J/cm2 when one 15 ns pulse from the 308 nm laser is used. The 15 ns pulse length is
chosen because the laser used is more stable for this pulse length. Increasing the pulse
length will increase the amount of radiation that the sample receives. This will cause the
28
temperature to be higher for the longer pulses length. Therefore, for longer pulse lengths
lower energy densities will need to be used to keep the sample from melting.
2.5.2 The 532 nm Melting Point
For the 532 nm experiments, to ensure that the regions studied will not be melted, an
initial set of experiments is performed using the 532 nm laser. For this experiment, 1 by
2
1 cm silicon samples implanted with boron at a dose of 2x10
15
2
ions/cm and an energy
of 5 KeV are used. Each sample is irradiated at a given energy density with one pulse.
2
For the 532 nm laser, the energy density is varied from 0.29 to 0.40 J/cm and the pulse
length is set at 20 ns. After all of the samples are laser annealed, the sheet resistance of
each sample is measured using a four-point probe. Plots of the sheet resistance versus
laser energy density along with the point when the surface reflectivity goes to one show
the maximum energy density which can be used to perform nonmelt laser annealing.
The results for the sheet resistances versus laser energy density using the 532 nm laser
are shown in Figure 2.8. The reflectivity versus laser energy density is plotted in Figure
2.9. The crystalline silicon melts at around 0.37 J/cm2 when one 20 ns pulse from the
532 nm laser is used.
29
Figure 2.1 This plot shows the temperature versus time seen at various depths in the
wafer during the NLA. The top curve is the temperature at the surface of the wafer. The
bottom curve is the temperature at 100 Å into the wafer.
30
Figure 2.2 This figure shows the temperature distribution in the wafer during one 20ns
pulse with the 532 nm laser. It also shows the beginning of the cool down after the pulse
is turned off (time > 2.0x10-8s).
31
Figure 2.3 This plot shows the temperature versus time seen at the surface of the wafer
when the sample is irradiated with multiple pulses at a frequency of 100Hz.
32
Figure 2.4 These plots are magnified views of the plot in Figure 2.3. This shows a more
detailed view of how the temperature is distributed over depth during the 532nm NLA.
33
21
10
1020
)
Portion of profile annealed during the
Boron (cm
3
308 nm anneal
1019
1018
1017
0
500
1000
1500
2000
2500
3000
Depth (Å)
Figure 2.5 Illustration of the approximate amount of the 5 KeV boron implant which is
annealed during a 308 nm NLA. The entire area is annealed during a 532 nm NLA.
34
Sheet Resistance (Ohms/sq)
2500
2000
1500
1000
500
0
0.3
0.4
0.5
0.6
0.7
2
0.8
Laser Energy (J/cm )
Figure 2.6 Sheet resistance vs laser energy density in 5 KeV, 1e15 B+/cm2 samples
irradiated with one 15 ns pulse using the 308 nm laser.
35
0.8
Reflectivity
0.7
0.6
0.5
0.4
0.3
0.2
0.4 0.45
0.5 0.55
0.6 0.65
0.7 0.75
0.8
Laser Energy Density (J/cm2)
Figure 2.7 Reflectivity versus laser energy density after one pulse with the 308 nm laser
on 5 KeV, 2e15 B+/cm2 samples.
36
Sheet Resistance (Ohms/sq)
1500
1000
500
0
0.3
0.32
0.34
0.36
0.38
0.4
Laser Energy Density (J/cm2)
Figure 2.8 Sheet resistance versus laser energy density for the 5 KeV, 2e15 B+/cm2
samples following one 20 ns pulse with the 532 nm laser.
37
0.8
Reflectivity
0.7
0.6
0.5
0.4
0.3
0.2
0.3
0.32
0.34
0.36
0.38
0.4
Laser Energy Density (J/cm2)
Figure 2.9 Reflectivity versus laser energy density for 5 KeV, 2e15 B+/cm2 samples
annealed with the 532 nm laser using a 20 ns pulse
CHAPTER 3
EXPERIMENTAL INVESTIGATIONS OF THE EFFECTS OF NLA ON BORON
IMPLANTED SILICON: 308 NM EXCIMER LASER
3.1 Overview
The main focus of this work is to investigate the effects of laser irradiation on boron
implanted crystalline silicon under conditions that do not cause melting of the implanted
region. How the laser affects the implanted region can be characterized by determining
the following: how the boron diffuses, how much of the boron becomes active, and how
the damage evolves during the laser anneal and with post-processing after the laser
anneal. These parameters have been shown to be dependent on the output wavelength of
the laser, the laser energy density of the incident beam, the length of the laser pulse, and
when multiple pulses are used, the time between pulses. Also of importance is the depth
of the damage and the boron during the laser anneal.
Since the laser energy densities where NLA can be performed have been determined
(Chapter 2), further experiments can now be carried out without worrying about melting
the silicon. This chapter (Chapter 3) and Chapter 4 give the experimental results and a
discussion of the results for samples annealed with the 308 nm laser and the 532 nm
laser, respectively. Chapter 5 elaborates on the effects of NLA on boron diffusion and
defect evolution by analyzing the effects of post-processing on samples given an NLA.
38
39
3.2 Experiments
3.2.1 Increasing the Number of Laser Pulses: 308 nm Laser, 5 KeV Boron Implant
A 5 KeV, 2e15 B+ ions/cm2 implant into a CZ grown <100> silicon wafer is
processed with a 308 nm XeCl excimer laser using one to 100 15 ns pulses at a laser
energy density of 0.6 J/cm2. Control samples receive an RTA step for 5 sec at 1040 °C
instead of the laser annealing. Indium contacts are made to the samples for sheet
resistance measurements using the Hall effect system. These samples are all analyzed
using SIMS, Hall Effect, and Plan-view TEM.
3.2.2 Increasing the Number of Pulses: 308 nm Laser, 1 KeV Boron Implant
A 1 KeV, 1015ions/cm2 B+ implant into a CZ grown <100> silicon wafer is processed
with the 308nm XeCl excimer laser. The 1 KeV implants received one or ten 15 ns
pulses at a constant energy density of 0.55 J/cm2. Following the NLA some samples
receive an RTA for 5 sec at 1040 oC. Control samples received the RTA and no NLA.
These samples are then analyzed using SIMS, Hall effect, and plan-view TEM. Indium
contacts are used for the Hall effect measurements.
3.3 5 KeV Results and Discussion
In order to investigate the effect that varying the number of laser pulses has on an
implant that is predominately deeper than the lasers absorption depth, an experiment
using the 308 nm laser is performed on samples implanted with boron at 5 KeV. This
experiment is described in section 3.2.2. The samples that receive the NLA are compared
to samples that just receive an RTA at 1040 oC
Figure 3.1 shows the SIMS profiles of the boron as-implanted, following the NLA,
and after the RTA. SIMS of the samples which received the NLA were the same as the
as-implanted profile showing that no detectable movement in the boron profile occurred
40
following the NLA when compared to the as-implanted profile. At a boron concentration
of 1018 ions/cm3, the boron moves 200 Å during the RTA.
Although no boron diffusion is detected in the SIMS, results show the sheet resistance
drops as the number of laser pulses increases with the most significant drop occurring
between 10 and 100 pulses (Figure 3.2). Thus, the NLA alone results in a sheet
resistance of 84 Ω/sq after 100 pulses compared with 520 Ω/sq in the sample just
receiving the RTA.
Figure 3.3 shows the plan-view TEM of the 5 KeV, 2e15/cm2 implants following
NLA and following the RTA. After the one pulse the formation of many tiny defects
begins to be detectable (top left picture). In this picture, a very grainy texture is observed
which is different from the as-implanted sample which shows no texture (much as this
TEM picture shows when printed). After ten pulses a high density of tiny dots become
visible in TEM (top right picture). These dots are slightly larger than those formed after
one pulse and the density appears to be slightly lower making it possible to note the
formation of individual defects. These dots grow into slightly larger defects with the
density decreasing again after 100 pulses (bottom left picture). As expected numerous
large loops were nucleated following the RTA alone (bottom right). It is immediately
obvious that the nonmelt laser anneal does not remove all of the damage from the
implanted samples. This makes sense based on the fairly shallow absorption depth of the
laser. The bulk of the damage and boron is well beyond the region that is heated by the
laser. Although the NLA did not cause boron diffusion, it is shown through the TEM that
the NLA alone has a very noticeable effect on the silicon interstitial diffusion. Thus the
NLA causes the nucleation of numerous tiny defects during one 15 ns laser pulse.
41
Examining the diffusion length of silicon interstitials over the temperature range from
1200-1400oC gives insight into why the interstitials have time to cluster during the 15 ns
anneal although the boron diffusion is minimal (Chapter 1). Since the boron is not
diffusing and causing an increase in width of the layers, the question remains as to why
the sheet resistance is decreasing during the NLA. In Chapter 6, the mobility and
activation of the layer is investigated. Understanding what causes the changes in the
mobility and activation will explain the drop in sheet resistance.
3.4 1 KeV Results and Discussion
Realizing that the 5 KeV implant produced a damage and boron profile far deeper than
the absorption depth of the 308 nm laser, a shallower implant energy of 1 KeV is chosen
for study. For this experiment, the effect of using multiple laser pulses is also studied.
Since the NLA alone from a single pulse decreases the sheet resistance of the boron
implanted layer without causing any boron diffusion, annealing the same area with more
pulses should result in lower sheet resistances without causing much if any boron
diffusion.
Figure 3.4 shows the SIMS of the 1 KeV samples as-implanted, after 10 laser pulses,
and after the 1040oC, 5 sec RTA. SIMS for the sample receiving one laser pulse is nearly
identical to the as-implanted profile. SIMS for the sample receiving ten laser pulses
shows that some boron diffusion occurs during the NLA alone. At a boron concentration
of 1018 ions/cm3 the boron moves 130 Å during the RTA.
Figure 3.5 shows the change in sheet resistance as the number of laser pulses is
increased for samples receiving the NLA and for the one receiving just the RTA. The
results show that the NLA alone results in a decrease in sheet resistance. The decrease in
42
sheet resistance following the NLA occurs with little change in the junction depth which
is measured at 1018 ions/cm3 (Figure 3.4).
Plan-view TEM pictures of the 1 KeV boron after 10 laser pulses and after the RTA
are shown in Figure 3.6. Figure 3.6 shows the NLA of ten laser pulses alone nucleates
numerous small loops (left picture). Figure 3.6 also shows the TEM after the RTA alone
(right picture). As is shown, the RTA results in fairly large loops compared to those
formed after the NLA. This change in defect density is qualitatively similar to that for
the 5 KeV samples.
The variations in diffusion and size of defects nucleated between the 5 KeV and 1
KeV samples can be attributed to the interaction of the laser beam with the damage and
boron following the implant. The laser used has an absorption depth around 70 Å. The
peak of the boron as-implanted profile is around 260 Å for the 5 KeV implant and 50 Å
for the 1 KeV implant. For the 1 KeV implant, the effect of the laser is distributed across
the bulk of the damage and dopant profile. While for the 5 KeV implant, the laser
interacts with less than a fifth of the damage and dopant profile. During the NLA the
surface is heated to 1200-1400oC for a few nanoseconds. This allows time for the silicon
interstitials to move around, but not the boron.
Due to the fact that the 1 KeV implant damage is contained primarily within the
absorption depth of the laser, the 1 KeV implanted samples will see higher temperatures
during the NLA than the 5 KeV implanted samples. This higher temperature in the 1
KeV results in the boron profile showing slight diffusion after 10 pulses at a boron
concentration of 1019 ions/cm3. Of course, this movement could also be attributed to
43
SIMS error. So perhaps the SIMS profiles do not provide a convincing argument that the
1 KeV implant sees higher temperatures than the 5 KeV implanted samples. However,
comparing the defect microstructures of the 5 KeV sample after 100 pulses with the 1
KeV sample after 10 pulses, shows that the defects are very similar in size and density
suggesting the 5 KeV sample sees the same average temperature as the 1 KeV samples
after 10 times the number of pulses.
3.5 Concluding Remarks
Basically, these results are presented here to convince the reader that it is important to
consider the absorption depth of the laser and how the temperature is distributed
compared to the implant profile when designing an annealing process using NLA. Also,
these results show that the NLA can be used to decrease the sheet resistance without
increasing the width of the implanted region. Due to a change in the availability of the
laser, a more complete study involving more laser pulses could not be carried out with the
308 nm laser. However, for the next set of experiments a large amount of extra material
is processed to account for any losses to the sample quantity occurring during sample
preparation for the various destructive techniques used for analysis. That said, in the next
chapter a similar set of experiments is performed using a 532 nm laser and one to 1000
pulses. The 532 nm laser has an absorption depth of between 5000 and 10000 Å in
crystalline silicon compared to 70 Å for the 308 nm laser.
44
21
10
as-implanted + NLA
0.0 J/cm2 w/RTA
Boron (cm
-3
)
1020
1019
1018
17
10
16
10
0
500
1000
1500
2000
2500
3000
Depth (A)
Figure 3.1 SIMS of 5 KeV, 2e15 B+/cm2 samples as-implanted and after the NLA with
308 nm laser, and after 1040oC,5 sec RTA.
45
Sheet Resitance (Ohms/sq)
3000
2500
2000
1500
1000
500
0
1
10
100
# of Laser Pulses
Figure 3.2 Sheet resistance number of laser pulses for 5 KeV, 2e15 B+/cm2 samples
following an NLA with the 308 nm laser at 0.6 J/cm2. using a pulselength 15 ns and a
frequency of 10 Hz.
46
Figure 3.3 Plan-view TEM for 5 KeV, 2e15 B+/cm2 samples following one pulse (top
left), 10 pulses (top right), 100 pulses (bottom right), and after a 1040oC, 5 sec RTA
(bottom right). For the NLA the 308 nm laser is used with a 15 ns pulse at a frequency of
10 Hz and a laser energy density at 0.6 J/cm2.
47
21
10
20
10
19
as-implanted
10 laser shots
RTA only
Boron (cm
-3
)
10
1018
0
100
200
300
400
500
Depth (A)
Figure 3.4 SIMS of the 1 KeV, 1e15 B+/cm2 samples as-implanted, after ten pulses, and
after a 1040oC, 5 sec RTA. The 308 nm laser with a 15 ns pulse at 10 Hz is used.
48
Sheet Resistance (Ohms/sq)
7000
6000
5000
4000
3000
2000
1000
0
1
# of laser pulses
10
Figure 3.5 Sheet resistance versus number of laser pulses for the 1 KeV, 1e15 B+/cm2
samples using the 308 nm laser with a 15 ns pulse at 10Hz. The point at 0 pulses
represents the sample that just received the 1040oC, 5 sec RTA.
49
Figure 3.6 Plan-view TEM of the 1 KeV, 1e15 B+/cm2 samples after 10 pulses using the
308 nm laser with a 15 ns pulse at 10Hz (left) and after the 1040oC, 5 sec RTA(right).
CHAPTER 4
EXPERIMENTAL INVESTIGATIONS OF THE EFFECTS OF NLA ON BORON
IMPLANTED SILICON: 532 NM RUBY:YAG LASER
4.1 Introduction
This set of experiments is designed to further investigate the effects of multi-pulse
nonmelt laser annealing on non-amorphizing doses of boron implanted in silicon. For
these experiments, a laser with a wavelength of 532 nm is used. This laser has an
absorption depth of 5000 to 10,000 Å which is nearly a thousand times deeper than that
of the 308 nm laser. To show how the absorption depths affect the outcome of the NLA,
the same 5 KeV implant used in Chapter 3 for the 308 nm NLA is also studied here with
a 532 nm NLA. The SIMS profiles, sheet resistances, and plan-view TEM results after
one to 1000 pulses are presented and compared to a conventional 1050oC spike anneal.
4.2 Increasing the Number of Pulses: 532 nm Laser, 500 eV Boron Implant
4.2.1 Experiment
A 500 eV, 1015 ions/cm2 B+ implant into a CZ grown <100> silicon wafer is annealed
with a 532 nm laser using one, 10, 100, and 1000 20 ns long pulses at an energy density
of 0.35 J/cm2. Recall from Figure 2.9 that above 0.35 J/cm2 at around 0.37 J/cm2 the
reflectivity of the surface (measured with a HeNe laser) plateaus indicating that surface
melting has occurred. The frequency of the laser is set at 100 Hz which allows time for
the sample to cool between pulses. The laser irradiates an area 1 x 1 cm2 with less than
3% variation in the beam over that area. Also, for the 532 nm laser, the absorption depth
into crystalline silicon is around 800 nm. These samples are compared to implanted
50
51
samples receiving a conventional 1050 oC spike anneal without any NLA. All samples
are analyzed using SIMS, Hall effect and plan-view TEM.
4.2.2 Results and Discussion
During a 20 ns pulse at 0.35 J/cm2, the temperature is expected to reach approximately
1200-1400 oC 500 to 10,000 Å deep into the sample while the bulk of the sample remains
at room temperature. After the 20ns pulse, the bulk then acts as a heat sink for the
surface region allowing the sample to cool down to below 500 oC in less than 0.1 ms.
Since the projected range of the 500 eV boron implant is at 2.5 nm, the entire boron
profile is expected to be heated during the NLA.
SIMS of the boron profiles as-implanted, following the NLA, and following the spike
anneal are shown in Figure 4.1. No diffusion is observed following one pulse. However,
the profiles following 10, 100 and 1000 laser pulses do show slight diffusion as the
profiles begin to break away from the as-implanted profile at a boron concentration
around 1020 ions/cm3. Diffusion does not appear to occur in the tail region of the profile
below 3x1017 ions/cm3 resulting in 21 to 25 nm junctions at 1018 ions/cm3. Although
some of the boron diffusion does occur during the NLA alone, most of the diffusion
occurs during the spike anneal resulting in the profile diffusing 170 Å at 1018 ions/cm3
resulting in a junction depth of 28 nm.
The sheet resistance measurements shown in Figure 4.2 are determined using Hall
effect measurements on square samples using indium contacts. Standard deviation for
the sheet resistance values for each sample is between 2 and 6%. Sheet resistance drops
to 800 Ω/sq and remains at around the same value following 10 pulses or more with the
NLA alone. The sheet resistance only drops to 2000 Ω/sq after the spike anneal alone.
52
Figure 4.3 shows the plan-view TEM for the 500 eV samples after the 1050 oC spike
anneal (bottom right). As shown, only a few loops 10-20 Å wide exist after the RTA.
Plan-view TEM of the samples following NLA show no defects. Since the NLA
nucleates a high density of small defects, it is not believed that the NLA alone completely
removes the implant damage but merely results in defects too small to detect with TEM.
Post processing of these samples will give more information as to what type of defects if
any remain after the NLA. Post-processing results are shown in Chapter 5.
4.3 Increasing the Number of Pulses: 532 nm Laser, 5 KeV Boron Implant
4.3.1 Experiment
A 5 KeV, 2 x 1015 ions/cm2 B+ implant into a CZ grown <100> silicon wafer is
annealed with a 532 nm laser using between one and 1000 20 ns long pulses at an energy
density of 0.35 J/cm2. These samples are compared to a sample that received the more
conventional 1050 oC spike anneal. SIMS, sheet resistance, Hall measurements, and
plan-view TEM are made on all samples.
4.3.2 Results and Discussion
Recall that since the projected range of the 500 eV boron implant is at 26 nm, the
entire boron profile is expected to be heated during the NLA. However, since the 5 KeV
implant is roughly 10 times deeper than the 500 eV implant the average temperature over
the region is expected to be less than that seen by the shallower implant. Boron profiles
measured with SIMS of the as-implanted, laser annealed, and the one processed with the
1050oC spike anneal are shown in Figure 4.4. No diffusion is observed following one,
10, 100, or 1000 pulses while substantial diffusion occurs in the sample receiving just the
spike anneal. These results are as expected since during the NLA the boron does not gain
enough energy from the temperature seen during the 20 ns pulse to diffuse any
53
measurable distance. Where, during the spike anneal, the boron does obtain enough
energy to diffuse.
The implant damage does however receive enough energy to diffuse during the NLA.
Figure 4.5 shows how the damage evolves as the number of laser pulses increases. The
top left picture is after one pulse, the top right after 10 pulses, the middle left after 100
pulses, the middle right after 1000 pulses, and the bottom picture after the 1050oC spike
anneal. Once again, although the boron does not diffuse, the silicon interstitials cluster
and form numerous tiny defects during the first pulse and those clusters grow into larger
defects as the number of pulses increases.
The sheet resistance measurements shown in Figure 4.6 are determined using Hall
effect measurements on square samples using indium contacts. Standard deviation for
the sheet resistance values for each sample is between 2 and 10%. The sheet resistance
drops to less than 100 Ω/sq during the NLA alone. It is interesting to note that the sheet
resistance does not continue to decrease after 100 laser pulses. This result can be
explained by examining the mobility and activation which is done in chapter 6.
Figure 4.7 shows a plot of the sheet resistance versus junction depth for the 500 eV
and 5 KeV experiments with the NLA compared to results from conventional processing
with the spike anneal. As shown, NLA will allow the formation of shallower junctions
with lower sheet resistances than conventional processing techniques.
54
22
10
as-implanted
one pulse
10 pulses
100 pulses
1000 pulses
RTA only
21
Boron (cm
-3
)
10
20
10
19
10
18
10
17
10
0
100
200
300
400
500
Depth (Å)
Figure 4.1 SIMS of the boron profiles as-implanted, following the NLA, and following
the 1050oC spike anneal for the 500 eV, 1e15 B+/cm2 samples.
55
Sheet Resistance (Ohms/sq)
3000
2500
2000
1500
1000
500
0
1
10
100
1000
# of Laser Pulses
Figure 4.2 Sheet resistance versus number of laser pulses for 500 eV, 1e15 B+/cm2
samples annealed with the 532 nm laser at 0.35 J/cm2 using a 20 ns pulse.
56
Figure 4.3 Plan-view TEM of the 500 eV, 1e15 B+/cm2 samples annealed with a 1050C
spike anneal.
57
1021
as-implanted and
1, 10, 100, 1000 shots
RTA only
Boron (cm
-3
)
1020
10
19
1018
10
17
1016
0
500
1000
1500
Depth (Å)
2000
Figure 4.4 SIMS of the boron profiles as-implanted, following the NLA, and following
the spike anneal for the 5 KeV, 2e15 B+/cm2 samples.
58
Figure 4.5 Plan-view TEM of the 5 KeV, 2e15 B+/cm2 samples annealed with the 532
nm laser at 0.35 J/cm2 using one, 10, 100, and 1000 pulses at 100Hz and 20 ns/pulse.
59
Sheet Resistance (Ohms/sq)
3000
2500
2000
1500
1000
500
0
1
10
100
1000
# of Laser Pulses
Figure 4.6 Sheet resistance versus number of laser pulses for 5 KeV, 2e15 B+/cm2
samples annealed with the 532 nm laser at 0.35 J/cm2 using a 20 ns pulse.
Sheet Resistance (Ohms/sq)
60
o
1050 C spike anneal
NLA only (100 pulses)
2000
1500
500 eV
1000
500
5 keV
0
50
100
150
200
250
XJ (nm)
Figure 4.7 Sheet resistance versus junction depth comparing NLA and the conventional
spike anneal for a 500 eV and a 5 KeV boron implant.
CHAPTER 5
EFFECTS OF POST-PROCESSING AFTER NONMELT LASER ANNEALING
5.1 Overview
This chapter shows and discusses the effects on boron diffusion and damage evolution
of post-processing of the NLA samples with rapid thermal anneals and furnace anneals.
After the NLA defects remain in the sample which are not visible in plan-view TEM.
Annealing the samples for longer times will allow the defects remaining after the NLA to
one, some, or all or the following: grow into defects (visible or submicroscopic),
recombine at the surface, recombine in the bulk, cluster with the boron, and/or enhance
the boron diffuse. Examining the defect structures and boron diffusion after postprocessing the samples which receive an NLA makes it possible to characterize and
further understand the types of defects that evolved during the NLA.
The time and temperature of the post-anneals all affect how the defects will evolve
and how the boron will diffusion. Device fabrication may also require various anneal
step following the NLA. Therefore, high temperature rapid thermal anneals and furnace
anneals are investigated.
5.2 High-Temperature Rapid Thermal Annealing after 308 nm NLA
5.2.1 Experimental Overview
A 5 KeV, 1e15 ions/cm2 B+ implant in silicon is processed with a single 15 ns laser
pulse at varying energies, 0.40 to 0.6 J/cm2, with the 308 nm laser. To help determine the
amount of remaining damage, some samples processed with the NLA also receive an
RTA for 5 sec at 1000 oC. Also, a 1 KeV, 1e15 ions/cm2 B+ implant in silicon is
61
62
processed with one or ten 15 ns laser pulses at a constant energy density of 0.55 J/cm2.
The 1 KeV implants processed with the NLA are also given a 1040oC, 5 sec RTA. This
allows us to observe the effects of using a laser anneal as a pretreatment for conventional
processing. These results are compared to a sample that just receive the RTA. The
samples are all analyzed using SIMS, Hall, and plan-view TEM.
5.2.2 5 KeV Results
Figure 5.1 shows the SIMS profiles of the boron as-implanted, following the RTA,
and after the NLA and RTA for the 5 KeV implants. A comparison of the SIMS between
the samples receiving just the RTA and the samples receiving the NLA and the RTA
shows the junction depth increases from 0.16 to 0.18 µm with very little difference in
diffusion for the NLA from 0.4 J to 0.6 J/cm2. The junction depth is measured at a boron
concentration of 1018 ions/cm3.
Figure 5.2 shows a plot of the sheet resistance versus laser energy density for the 5
KeV implants. Results show the sheet resistance drops to around 150 Ω/sq for samples
receiving the NLA and the RTA compared with the samples just receiving the RTA. This
30% drop in sheet resistance comes with only a 10% increase in the junction depth.
In order to understand the reasons for the boron diffusion and drop in sheet resistance,
the samples are analyzed using plan-view TEM. For the 5 KeV implants, samples
receiving the RTA, plan-view TEM results show the NLA strongly affects the extended
defect density producing a larger density of smaller defects (Figure 5.3). For comparison,
plan-view TEM following just the 0.4 J/cm2(top left) and 0.6 J/cm2(top center) NLA are
also shown. The formation of numerous small defects (represented by the white dots)
following the 0.4 J/cm2 and 0.6 J/cm2 NLA shows the dramatic effect of the laser
preanneal on the defect nucleation. Figure 5.3 shows the defect evolution in samples
63
receiving the NLA at various energies followed by the RTA. The top right picture is for
the sample receiving just the RTA and no NLA. It shows the formation of numerous half
loops. (Half loops are loops that unfault on the surface.) The bottom pictures from left to
right are for the samples which receive the 0.4 J/cm2 NLA followed by the RTA, the 0.5
J/cm2 NLA followed by the RTA, and the 0.6 J/cm2 NLA followed by the RTA. From
these pictures, the number of the loops which extend to the surface (the half loops) is
shown to decrease as the laser energy is increased. Note that the half loops have a nearly
constant diameter around 0.1um for all four samples. Figure 5.4 plots the percentage of
half loops extending to the surface versus laser energy.
Also from Figures 5.3 it is shown that as the laser energy increases the density of the
defects increases while the size of the defects decreases. This is quantified in Figure 5.5
which shows the density of the defects versus laser energy. Recall that there is a drop in
sheet resistance beyond that expected due to the increase in junction depth. This drop in
sheet resistance must be due to an increase in mobility or an increase in carrier activation.
Since from Figures 5.3 and 5.5, the number of defects visible in plan-view increases it is
not immediately obvious why there would be a drop in sheet resistance unless it is due to
an increase in activation. More defects would typically be expected to cause a decrease
in the mobility which would increase the sheet resistance. A possible explanation at this
time may be deduced from the previous figures. Recall from Figure 5.3 that as the
number of defects increases the average size of the defects decreases resulting in fewer
larger defects that extend to the surface. It is possible that the loops which unfault on the
surface have scattering sites along the entire area (πr2) of the defect making the number
of scattering sites proportional to r2. However, the smaller more perfect loops will have
64
scattering sites only along their circumference (2πr) making the number of scattering
sites proportional to r. Hence, less scattering sites exist after the NLA resulting in an
increase in the mobility. It is also possible that the loops which exist at around the
projected range of the boron implant have little effect on the mobility compared to the
effects of ionized impurity scattering or neutral scattering. The effects of the loops on
mobility and activation will be investigated further in Chapters 6 and 7.
5.2.3 1 KeV Results
SIMS for the 1 KeV implants are shown in Figure 5.6. SIMS following an NLA of 10
pulses with no RTA is also shown for comparison. For the 1 KeV implants, SIMS of the
samples receiving one laser pulse plus the RTA is nearly identical to the RTA alone.
Figure 5.6 shows that the NLA of ten laser pulses prior to the RTA decreases the boron
diffusion while one laser pulse shows no noticeable effect. This is contrary to the 5 KeV
SIMS results which show that the boron profile diffuses more when given an NLA prior
to the RTA, SIMS results of the 1 KeV boron show that the 10 pulses with the NLA prior
to the RTA actually decreases the boron diffusion.
Figure 5.7 shows the change in sheet resistance as the number of laser pulses increases
for samples receiving the NLA followed by the RTA for the 1 KeV implants. The results
following the NLA alone are presented for comparison. The sheet resistance following
the RTA alone is 1100 Ω/sq. It drops to 220 Ω/sq when receiving the 10 pulse NLA
prior to the RTA.
Plan-view TEM pictures of the 1 KeV boron after 10 laser pulses, after the RTA, and
after 10 laser pulses plus the RTA are shown in Figure 5.8. The left picture shows that
the NLA of ten laser pulses alone nucleates numerous small loops. The picture on the
65
right shows that the ten pulse NLA prior to the RTA reduces the final loop density when
compared with the RTA alone (center picture). This change in defect size is qualitatively
similar to that for the 5 KeV samples. However, the NLA prior to the RTA results in an
increase in the loop density for the 5 KeV samples and a decrease in the loop density for
the 1 KeV samples.
The variations in loop densities and diffusion can be attributed to the interaction of the
laser beam with the damage and boron following the implant. Recall, that the laser used
has an absorption depth around 70 Å. The peak of the boron as-implanted profile is
around 260 Å for the 5 KeV implant and 50 Å for the 1 KeV implant. For the 1 KeV
implant, the effect of the laser is distributed across the bulk of the damage and dopant
profile. While for the 5 KeV implant, the laser interacts with less than a fifth of the
damage and dopant profile. During the NLA the surface is heated to 1200-1400oC for a
few nanoseconds. This allows time for the silicon interstitials to move around. Thus
during one laser pulse interstitials diffuse to the surface where they recombine while
some remain behind in clusters.
5.2.4 Discussion
In summary, for the 5 KeV implants we see that a laser preanneal does not anneal all
of the damage from the implant. However, the NLA significantly alters the defects
present after subsequent anneal and produces a decrease in sheet resistance as the laser
energy density is increased.
For the 5 KeV implant, during one laser pulse a region around 70 Å thick rich in
interstitials is heated resulting in the nucleation of numerous small interstitial clusters.
When followed with an RTA, these interstitial clusters grow and act as traps for
interstitials which would normally recombine at the surface. This increases the number
66
of interstitials available to contribute to TED and defect formation during post-annealing.
As shown in Figure 5.1 similar diffusion occurs for all laser energies following the RTA.
Also, although the number of loops increases as the number of laser pulses increases, the
number of interstitials contained in the loops after the RTA is roughly the same for each
sample (Figure 5.3). Since the bulk of the damage is not annealed during the NLA and a
similar number of interstitials remain, post-processing of the samples receiving the NLA
results in similar boron diffusion.
For the 1 KeV, the bulk of the interstitials and boron are within 70 Å of the surface. A
possible scenario is that this high concentration of impurity atoms (which means more
electrons) decreases the absorption length of the silicon reducing the depth of the heated
layer. During the first laser pulse, numerous small defects are nucleated in this thin
region with the size of the defect being no larger than the width of the heated region.
During subsequent laser pulses the width of this heated region increases along with the
size of the defects. After ten laser pulses the defects are large enough to be detected in
the TEM. Meanwhile, during each pulse interstitials have been making it to the surface
where they recombine resulting in fewer interstitials available to form loops and
contribute to TED during post-annealing.
5.3 High-temperature rapid thermal anneals after 532nm NLA
5.3.1 Experimental Overview
For these experiments, samples are implanted with either 500 eV, 1e15 B+ ions/cm2 or
5 KeV, 2e15 B+ ions/cm2. They are then given an NLA with the 532 nm laser. The
energy density is set at 0.35 J/cm2. The number of pulses is varied from 1 to 1000. The
samples are then post-processed with a conventional 1050 oC spike anneal. Results are
compared to a sample with the same implant conditions that just receive the spike anneal.
67
5.3.2 5 KeV Results and Discussion
For the 5 KeV samples, SIMS results show that the sample receiving one pulse plus
the RTA diffuses slightly further than the sample which receives the RTA alone. The
sample receiving 10 pulses plus the RTA diffuses about the same if not slightly less than
the sample receiving just the RTA (See Figure 5.9). The samples receiving 100 or 1000
pulses plus the RTA are shown to diffuse only slightly compared to the as-implanted
profile.
The sheet resistances versus number of laser energy pulses for the samples receiving
the NLA plus the RTA are compared to the samples receiving just the NLA in Figure
5.10. The sheet resistance at 0 J/cm2 on the NLA plus RTA line is for the sample
receiving only the RTA. As shown, the sheet resistance decreases as the number of laser
pulses increases and plateaus at around 150 Ω/sq after 10 pulses. Also, for the sample
receiving one pulse plus the RTA the sheet resistance actually increases while no
improvement in the sheet resistance occurs in the samples receiving 10 or more pulses
plus the RTA. The increase in sheet resistance for the sample receiving one pulse plus
the RTA must be due to either a decrease in activation or mobility. This will be
discussed in Chapter 6.
Plan-view TEM for these 5 KeV implants processed with the NLA and RTA are
shown in Figure 5.11. The upper left picture is for the sample which just receives the
RTA, the upper right picture is following one pulse plus the RTA, and the bottom picture
is following 10 pulses plus the RTA. The samples receiving 100 or 1000 pulses plus the
RTA show no defects in plan-view TEM. It is interesting to note that similar SIMS
profiles are obtained for all of the samples shown in Figure 5.11 although the defect
structure is substantially different in each sample.
68
Since boron is believed to need to react with an interstitial to diffuse, having more
interstitials available usually means more boron diffusion. This must mean that prior to
or during the RTA, a similar number of free interstitials exist or are made available in
each of the following samples: as-implanted, one pulse, and ten pulses. While since no
diffusion occurs for the samples receiving 100 or 1000 pulses when processed with an
RTA it appears that there are not any interstitials available to form mobile pairs and react
with the boron during the RTA. Thus the defects visible after the 100 or 100 pulses NLA
must have dissolved and recombined at the surface, formed microscopic interstitial
clusters, or clustered with boron since they did not cause boron diffusion and are no
longer visible in the TEM following the RTA. Since no loops exist in some of these
samples, analyzing the boron activation for all of the samples should give information on
what type of defects exist prior to the RTA. This will be discussed in Chapter 6.
5.3.3 500 eV Results and Discussion
For the 500 eV implants, SIMS results show that the boron diffusion is similar to the
results for the 5 KeV implants (Figure 5.12). The sample receiving one pulse plus the
RTA is nearly identical to the sample receiving the RTA alone while the sample
receiving 10 pulses plus the RTA diffuses slightly less than the sample receiving only the
RTA. The samples receiving 100 or 1000 pulses plus the RTA diffuse the least and only
diffuse slightly when compared to the as-implanted profile.
The sheet resistances versus number of laser pulses for the 500 eV implants processed
with the NLA and RTA are presented along with the results just after the NLA in Figure
5.13. For these samples, the RTA increases the sheet resistance. Since diffusion occurs
during the RTA a decrease in the sheet resistance is typically expected. This change in
69
sheet resistance must be related to the changes in activation of mobility. This will be
discussed in Chapter 6.
The plan-view TEM of the samples after the RTA show no defects for any samples
receiving the NLA prior to the RTA. The only sample which had any visible defects
though few is the sample receiving just the RTA. The plan-view TEM picture for the
sample receiving just the RTA is shown in Figure 5.14. There are at least two
explanations as to why the defects are not visible in any of the plots except for the sample
receiving just the RTA. The explanations do not conflict with each other and when used
together further decrease the possibility of there being any visible defects. If 1000 pulses
is enough to remover most of the damage for the 5 KeV implants, it is very likely that the
NLA will remove most of the implant damage during 100 to 1000 pulses for the 500 eV
samples. Interstitials in the 500 eV implanted sample should logically have around a
tenth of the distance to travel to reach the surface as the 5 KeV implanted samples.
Therefore, they should only need a tenth of the time to disappear. The other explanation
for the lack of visible damage comes from analyzing the plan-view TEM for other
samples processed with the NLA. It is shown in Figure 5.11 that the NLA causes a high
density of smaller defects to evolve in samples. It is also shown that these defects are
smaller on average in samples receiving the NLA prior to the RTA. So, if the defects are
only 30 to 50 Å in the 500 eV sample after only the RTA (Figure 5.14), then the defects
would be even smaller and less likely to show up in TEM after the NLA.
By looking at the SIMS for these samples more insight into the type of defects if any
remain can be gained (Figure 5.12). Since the sample receiving one pulse plus the RTA
diffuses about the same as the sample receiving just the RTA it is most likely that one
70
pulse does not remove much if any of the available interstitials. It merely allows it to
form tiny clusters. Ten pulses prior to the RTA results in less diffusion compared to the
RTA, so this means less interstitials are probably available to add the TED. These
interstitials could have recombined at the surface, clustered with the boron, or clustered
into more stable microscopic interstitial loops so as not to be available for boron diffusion
during the RTA. Since the samples receiving 100 and 1000 pulses prior to the RTA
diffuse only slightly into the sample, it appear that very few free interstitials exist
following the 100 and 1000 pulse NLA. Once again, the defects could be hanging out in
clusters instead of running to the surface to recombine. However, it is believed that most
of the interstitials have diffused to the surface during the NLA. The few that remain most
likely make it to the surface during the RTA. Further processing and SIMS analysis of
these samples at lower temperatures for longer times would give even more detail as to
how many interstitials remain, but this will be left for possible future studies.
One point which has been left out of the discussion of the 500 eV samples is the dose
loss which occurs during the RTA. Although the tails of the 5 KeV and 500 eV profiles
diffuse similarly, the 500 eV samples exhibit serious dose loss with the average dose
dropping 50% during the RTA. Since the boron has to go somewhere, the dose loss
during the RTA must result in a pile up of the boron at the silicon/oxide interface and/or
and increase in the boron in the oxide. For the sample receiving just the RTA or one
pulse plus the RTA there would be interstitials around to enhance the diffusion.
However, for the samples receiving 100 and 1000 pulses the interstitial population should
be reduced enough so that which is typically called transient enhanced diffusion (TED) is
dramatically reduced if not eliminated. So, if the interstitials which cause TED are gone,
71
then what drives the boron diffusion which results in the dose loss in the samples
receiving 100 or 1000 pulses prior to the RTA? Perhaps, the phenomena call boron
enhanced diffusion (BED) is occurring. The 500 eV implant does after all result in boron
concentrations above 1e21 /cm3 and one of the requirements for BED is a high
concentration of boron. The diffusion behavior believe it or not helps explain the boron
activation which occurs during the NLA and will be discussed in Chapter 6.
5.4 Furnace Anneals and Damage Evolution
5.4.1 308nm NLA
These results are presented merely to further illustrate the dramatic effect that NLA
has on defect evolution. The 5 KeV samples receiving the NLA with the 308 nm laser
are post-processed using a 750oC furnace anneal from 15 to 90 minutes. The effects of
NLA prior to furnace annealing on the defect microstructure are compared to samples
which receive only the furnace anneal. The results from plan-view TEM are shown in
Figure 5.15. The top left picture is for the 5 KeV sample processed with just a 750oC, 15
min furnace anneal. The picture shows the formation of numerous 311 defects (the rodlike defects) and a few large dislocation loops. After 45 and 90 minutes none of the 311
defects remain and only one or two large loops are visible in TEM. The upper right
picture shows the defect evolution following the NLA and a 15 min, 750oC furnace
anneal. In this picture a high density of small loops have evolved. Comparing the top
two pictures makes it immediately obvious that the NLA is having a significant effect on
the defect evolution for this implant and NLA condition. The bottom two pictures from
left to right are for the samples receiving the NLA plus a 45 min, 750oC furnace anneal
and the NLA plus a 90 min, 750oC furnace anneal. The pictures show that the loops
72
nucleated during the NLA grow into slightly large loops as time increases, but remain
relatively stable between 45 and 90 minutes.
5.4.2 532nm NLA
Figure 5.16 shows the plan-view TEM for the 5 KeV samples processed with the 532
nm laser as-implanted (top left), after a 750oC, 15 min furnace anneal (top right), a 10
pulse NLA (center left), a 1000 pulse NLA (bottom left), a 10 pulse NLA plus the
furnace anneal (center right), and a 1000 pulse NLA plus the furnace anneal (bottom
right). TEM needs to be redone then the discussion added. Not sure it adds much either.
Could also add 900C furnace anneal junk here. 900C does not add much. Hall effect
exists for all, but no SIMS.
5.5 Conclusions
The NLA prior to the RTA can reduce the amount the boron diffuses into the sample.
The NLA prior to the RTA can also reduce the amount of interstitials around to form
defects during the RTA. Also, the NLA prior to the RTA results in a dramatic change in
the defects which evolve in the samples. The microscopic change is fairly obvious in the
TEM: the NLA causes a high density of loops to evolve in samples which may have
otherwise evolved 311s or larger loops. Also, although not evident in the samples
receiving 100 or 1000 pulses prior to the RTA, the SIMS profiles for the samples
receiving 10 or less pulses prior to the RTA do show the broad diffusion shoulder
characteristic of high dose boron implants. This implies that much of the surface boron is
trapped in boron interstitial clusters. Of course, BICs imply deactivation which is one of
the subjects of the next chapter, Chapter 6. In Chapter 6 the SIMS profiles and defect
microstructure will be discussed in more detail as the boron diffusion and defect
structures both influence the activation and mobility of the layer.
73
10
21
20
10
19
10
18
10
17
10
16
Boron (cm
-3
)
10
as-implanted
0.0 J/cm2 w/RTA
0.4 J/cm2 w/RTA
0.5 J/cm2 w/RTA
0.6 J/cm2 w/RTA
0
50
100
150
200
250
300
Depth (nm)
Figure 5.1 SIMS profiles following NLA and 1000oC, 5sec RTA for 5 KeV are shown.
1e15 B+ ions/cm2 samples processed with the 308 nm laser.
74
Sheet Resistance (Ohms/square)
240
220
200
180
160
140
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2
Energy Density (J/cm )
Figure 5.2 Sheet Resistance vs. Laser Energy Density following 1000oC, 5sec RTA for 5
KeV. 1e15 B+ ions/cm2 samples processed with the 308 nm laser.
75
Figure 5.3 TEM following 0.4 J/cm2 NLA, following 0.6 J/cm2 NLA, and following the
RTA (top pictures from left to right), and TEM of samples receiving 0.4, 0.5, or 0.6 J/cm2
NLA followed by RTA (bottom pictures from left to right).
% of Loops Extending to Surface
76
100
80
60
40
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
2
Laser Energy Density (J/cm )
Figure 5.4 Percentage of loops extending to the surface versus laser energy density for
1000oC, 5sec RTA of 5 KeV. 1e15 B+ ions/cm2 samples processed with the 308 nm
laser.
8x10
9
6x10
9
-2
Loop Density (cm
)
77
4x109
2x10
9
0
0.1
0.2
0.3
0.4
0.5
0.6
2
Laser Energy Density (J/cm )
Figure 5.5 Defect density versus laser energy density for 1000oC, 5sec RTA of 5 KeV.
1e15 B+ ions/cm2 samples processed with the 308 nm laser.
78
21
10
20
10
19
10
18
Boron (cm
-3
)
10
as-implanted
10 laser shots
10 shots + RTA
RTA only
0
100
200
300
400
500
Depth (Å)
Figure 5.6 SIMS of 1 KeV, 1015 ions/cm2 B following 10 laser pulses, with 1040oC, 5
sec RTA, and 10 pulse plus 1040oC, 5 sec RTA.
79
Sheet Resistance (Ohms/sq)
6000
5000
NLA only
with RTA
4000
3000
2000
1000
0
1
10
# of Laser Pulses
Figure 5.7 Sheet resistance versus number of laser pulses for 1 KeV, 1015/cm2 B for
samples receiving just the NLA (NLA only) and those processed with 1040oC, 5 sec RTA
(with RTA).
80
Figure 5.8 Plan-view TEM of 1 KeV, 1e15/cm2 boron implanted silicon following (from
left to right) 10 shots, RTA only, 10 shots plus RTA.
81
21
10
as-implanted
one pulse plus RTA
10 pulses plus RTA
100 and1000 pulses
plus RTA
RTA only
-3
Boron (cm
)
1020
1019
1018
1017
0
500
1000
1500
2000
Depth (Å)
Figure 5.9 SIMS of 5 KeV, 2e15 B+ ions/cm2 samples following NLA with the 532 nm
laser using a 20 ns pulse length at 100 Hz and 1050oC spike anneal compared with the
sample receiving just the spike anneal.
82
Sheet Resistance (Ohms/sq)
3000
2500
NLA only
2000
with 1050oC
spike anneal
1500
1000
500
0
1
10
100
1000
# of Laser Pulses
Figure 5.10 Sheet resistance versus number of laser pulses of 5 KeV, 2e15 B+ ions/cm2
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 Hz
and/or 1050oC spike anneal.
83
Figure 5.11 Plan-view TEM of 5 KeV, 2e15 B+ ions/cm2 samples following RTA alone,
one pulse plus RTA, and 10 pulses plus RTA. The NLA is at 0.35 J/cm2 with the 532 nm
laser using a 20 ns pulse length at 100 Hz. The RTA is a 1050oC spike anneal.
84
22
10
as-implanted
RTA only
1 pulse + RTA
10 pulses + RTA
100 pulses + RTA
1000 pulses + RTA
21
Boron (cm
-3
)
10
20
10
19
10
18
10
17
10
0
100
200
300
400
500
Depth (Å)
Figure 5.12 SIMS of 500 eV, 1e15 B+ ions/cm2 samples following NLA with the 532
nm laser using a 20 ns pulse length at 100 Hz and 1050oC spike anneal compared with
the sample receiving just the spike anneal.
85
Sheet Resistance (Ohms/sq)
3000
NLA only
2500
with 1050oC
spike anneal
2000
1500
1000
500
0
1
10
100
1000
# of Laser Pulses
Figure 5.13 Sheet resistance versus number of laser pulses of 500 eV, 1e15 B+ ions/cm2
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 Hz
and/or 1050oC spike anneal.
86
Figure 5.14 Plan-view TEM of the 500 eV, 1e15 B+/cm2 sample annealed with a 1050oC
spike anneal.
87
Figure 5.15 Plan-view TEM of 5 KeV, 1e15 B+ ions/cm2 samples after 750oC furnace
anneal (top left), NLA plus 750oC, 15 min furnace anneal (top right), NLA plus 750oC,
45 min furnace anneal (bottom left), and NLA plus 750oC, 90 min furnace anneal
(bottom right). The NLA is with the 308 nm laser using one 15 ns pulse at 0.6 J/cm2.
88
Sheet Resistance (Ohms/sq)
2500
NLA only
plus FA
2000
1500
1000
500
0
1
10
100
1000
# of Laser Pulses
Figure 5.16 Sheet resistance for the 5 KeV, 2e15/cm2 samples receiving the 532 nm
NLA and/or the 750oC furnace anneal.
CHAPTER 6
EFFECTS OF NLA ON MOBILITY AND ACTIVATION
6.1 Introduction
The focus of this work is to explain the effects of NLA on silicon implanted with a
high dose (>1e15/cm2) of boron. This requires understanding the effect of the NLA on
the electrical properties of the boron-implanted layer. It also requires understanding how
the electrical and physical properties of the layer interact. In this chapter the mobility and
activation data for the experiments presented in chapters 3 through 5 will be presented
and discussed. The mobility, hole density, and sheet resistance are all measured using the
Hall effect and a hall factor of 0.7 as described in Chapter 1. The results are presented
and compared to the plan-view TEM and SIMS results from Chapters 3 through 5. SIMS
profiles along with Hall measurements allow determination of the actual amount of boron
which is inactive in the annealed layer. Analyzing SIMS profiles, and the defect
microstructure, along with knowing how much inactive boron exists can help determine
if boron clustering is occurring. Knowing the type of defects in the system and the
distribution of the defects is essential to predicting the electrical properties of the layer.
First, the various factors which affect the activation and deactivation are discussed.
Then, the mobility and sheet resistance data are examined. Finally, the effect of the loops
on the mobility and activation is shown and discussed.
89
90
6.2 Experimental Results
6.2.1 The 308 nm Experiments
Samples implanted with boron at 5 KeV, 2e15 ions/cm2 or 1 KeV, 1e15 ions/cm2
are annealed using a 308 nm NLA at a constant energy density of 0.6 J/cm2. The pulse
frequency is set at 10 Hz and the pulse length at 15 ns. To further understand the effects
of NLA on the boron implanted samples, some of the samples receiving the NLA and a
sample receiving no NLA are annealed with a 1040oC, 5 sec RTA.
Hall effect measurements can be made on all of the samples after the RTA. However,
for the 5 KeV samples receiving one and ten laser pulses Hall effect measurements
cannot be made. The heavy damage remaining from the implant is believed to cause
significant error in the measurements. For example, if ohmic contacts can be made to the
material, the currents measured are found to vary by more than 10% between the contacts
for a fixed voltage. This nonuniformity in resistance between the contacts makes it
impossible to obtain any useful information from the Hall measurements. For these
samples the mobility and the hole densities are set to zero. Figure 6.1 shows plots of the
hole mobility (top) and the hole density (bottom) as a function of the number of laser
pulses for the 5 KeV samples. These plots show the NLA has no measurable effects on
the 5 KeV samples until 100 pulses. After 100 pulses with the NLA, the mobility and the
hole density both increase. However, when followed with an RTA, the mobility
decreases slightly from 43 to 40 cm2/V-s while the hole density drops by nearly 75%.
Figure 6.2 shows the percent activation as a function of laser pulses for the 5 KeV
samples. To determine the activation, the active dose (the hole density) is divided by the
implant dose of 2e15 ions/cm2. This dose is also the dose calculated from the SIMS
profiles shown in Chapter 3.
91
Figure 6.3 shows plots of the hole mobility (top) and the hole density (bottom) as a
function of the number of laser pulses for the 1 KeV samples. For the 1 KeV implants,
the 308 nm NLA alone causes the mobility and the hole density to increase as the number
of laser pulses increases. However, post-processing with the RTA causes an increase in
the mobility and a decrease in the hole density. The plots for the activation are shown in
Figure 6.4. The top plot is the hole density divided by the implant dose. The bottom plot
is for the hole density divided by the actual implanted dose of 7.4e14 ions/cm2. The dose
is calculated by integrating the SIMS profiles of Chapter 3. According to the SIMS
profiles, no dose loss is found to occur during the NLA or RTA. This means the same
dose is used to determine the activation for all annealing conditions. Dose loss does
occur during the boron implantation step. The dose loss during the implant is found to be
26% of the implanted dose. Using the dose of the implant (1e15/cm2) will tell you the
efficiency of activation at that implant dose. However, the actual dose which makes it
into the sample must be used to accurately describe the actual electrical activation in the
implanted layer.
6.2.2 The 532 nm Experiments
This next set of experiments uses the 532 nm laser for the NLA. For these
experiments, a constant energy density of 0.35 J/cm2, a pulse frequency of 100 Hz, and a
pulse length of 20 ns, is used. The implant conditions are 5 KeV, 2e15 B+ ions/cm2 and
500 eV, 2e15 B+ ions/cm2. The number of pulses is varied from one to 1000. Some of
the samples receiving the NLA and some which do not receive the NLA are postprocessed with a 1050oC spike anneal. The plots are prepared to show how the NLA and
post-processing affect the mobility and hole density.
92
Figure 6.5 shows the plots of the mobility and hole density versus number of laser
pulses for the 5 KeV implants. Figure 6.6 shows a plot of the percent activation versus
number of laser pulses for the 5 KeV implants. For this plot, the percent activation is
determined by dividing the hole density by the implant dose of 2e15 ions/cm2 which is
also the dose calculated from SIMS profiles. As shown, the mobility and activation
increase as the number of laser pulses increases. Post-processing with the RTA,
however, causes deactivation and for the most part an increase in the hole mobility.
Figure 6.7 shows the plots of the mobility and hole density versus number of laser
pulses for the 500 eV implants. The plots for the activation are shown in Figure 6.8. The
top plot is the hole density divided by the implant dose of 1e15 ions/cm2, and the bottom
plot is for the hole density divided by the actual implanted dose calculated from the SIMS
profiles. The as-implanted dose is found to be 7.0e14/cm2. Once again, dose loss occurs
during the implant. However, for this implant dose loss also occurs during the
subsequent annealing steps.
Figure 6.9 shows the amount of dose lost during the NLA and RTA steps. The top
plot shows the change in dose during the NLA and the NLA followed by the RTA. The
bottom plot shows the percentage of dose lost during the RTA. These quantities will
become more important when analyzing the effect of the NLA and RTA on boron
activation.
6.3 Discussion
6.3.1 Overview
For the percent activation plots, dividing the hole density by the implant dose shows
the negative effect of the dose loss during implantation on the total boron activation.
However, dividing the hole density by the actual dose that makes it into the sample
93
allows for the calculation of the actual amount of inactive boron left after the anneals.
This quantity is more relevant to understanding the electrical characteristics of the
implanted layer.
All of the plots show the NLA alone causes the mobility to increase and the activation
to increase as the number of laser pulses increases. Both are positive effects that result in
lower sheet resistances for the individual cases. However, when the results from all of
the experiments are plotted together versus sheet resistance it becomes apparent that the
hole density is dominating the change in sheet resistance. Figure 6.10 shows the plots for
the hole density and hole mobility versus sheet resistance. The plot for the hole density
versus sheet resistance shows how increasing the hole density decreases the sheet
resistance. However, the plot for the mobility versus sheet resistance shows no trend.
Thus, the changes in sheet resistance as a whole appears to be dominated by the change
in the hole density (active boron dose) and not by the mobility. Lets investigate whether
this change as a whole can be explained by the defects visible in plan-view TEM
presented in Chapters 3 and 4.
Plots of the mobility versus the loop dose and interstitial dose are shown in Figure
6.11. Plots of the percent activation versus the loop density and interstitial density are
shown in Figure 6.12. The mobility and the activation show no strong trends when
compared to the interstitial densities and loop densities observed using TEM. This is
surprising, since it is generally thought that more defects would mean more scattering
sites, and more scattering sites would cause a decrease in the mobility.
6.3.2 Boron Activation, Deactivation, and Precipitation
So far, the only obvious trend is that the sheet resistance is dominated by the changes
in activation. This section will further investigate the causes of the boron activation and
94
deactivation. Figures 6.1 through 6.8 show that in general, the RTA after the NLA
decreases the hole density. A decrease in the hole density means that boron deactivation
is occurring. Comparing the bottom plot in Figure 6.8 with Figure 6.6 shows that only
35% of the boron is being activated during the NLA of the 500 eV samples versus 95%
activation in the 5 KeV samples. There are only three cases where the RTA after the
NLA does not cause boron deactivation. These are for three of the 500 eV samples.
These samples are the ones given one, ten, or 100 pulses prior to the RTA.
Plan-view TEM of the 5 KeV as well as the 500 eV samples shows that no defects
exist in the 5 KeV samples after 1000 pulses or in the 500 eV samples after 10, 100 and
1000 pulses (Chapter 4). Also, SIMS results show that boron diffusion into the samples
during the RTA occurs only slightly for the 5 KeV and 500 eV samples that receive a 100
or 1000 pulse NLA prior to the RTA (Chapter 4). What the results for the 5 KeV and 500
eV samples imply is that interstitials are not available after the 100 and 1000 pulse NLA
to significantly contribute to boron diffusion (TED) or extended defect formation.
In the 500 eV samples, if most of the interstitials were gone then this would mean that
no interstitials should be available to form boron interstitial clusters. This raises a
question on why the boron is not continuing to activate as the number of laser pulses
increases. With so few interstitials around, a boron rich region, and a high temperature
anneal, a possible explanation might be boron precipitation. The 500 eV implant results
in a significantly higher boron concentration of 2 to 3e21 B+ ions/cm3 versus 7e20 B+
ions/cm3 for the 5 KeV implants. During one pulse interstitial clusters form and boron
activates. During the next nine pulses, the boron begins to diffuse and the interstitial
clusters grow. Somewhere between 10 and 100 pulses, the interstitial clusters have
95
dissolved or have been consumed by the surface. The lack of interstitials available, and
the high boron concentration suggests that if any boron interstitial clusters are forming
they would be predominately boron after 100 and 1000 pulses.
This does seems to suggest the possibility that these boron clusters are actually boron
precipitates, which form during 10 to 100 pulses with the NLA. These precipitates would
be sub-microscopic and evenly distributed in the layer. This distribution could produce a
uniform strain making them undetectable during TEM analysis.
Is boron precipitation realistic? Recall from the SIMS that the boron peak
concentration in the 500 eV samples is 2 to 3e21 B+ ions/cm3 while it is only 7e20 B+
ions/cm2 in the 5 KeV samples and 1e21 B+ ions/cm3 in the 1 KeV samples. Since the
solid solubility limit is around 2e20/cm3 for the temperatures reached during the NLA,
this concentration is certainly high enough to result in boron precipitation in the 500 eV
samples.
However, precipitation is unlikely the cause since the following scenario during the
RTA would have to occur: During the RTA, the precipitates would have to dissolve
which would supply boron to the layer and not interstitials. Thus resulting in an increase
in boron activation without TED. Unfortunately, a 1040oC, 5 sec RTA is not likely to
supply enough energy to break up a BIC let alone dissolve a precipitate. Also, the 5 KeV
boron concentration is also high enough (2e20/cm3 at the surface and 7e20/cm3 at its
peak) that boron precipitation would occur. Since nearly 100% of the 5 KeV implant can
be activated it is even more unlikely that precipitates formed during the NLA of either
set. So, the dissolution of boron precipitates is not likely to be a reasonable explanation
for the boron activation during the RTA
96
6.3.3 Boron Activation, Deactivation, Interstitials, and Diffusion
Since precipitation is probably not the answer, the amount of interstitials available and
the boron diffusion occurring may help explain the deactivation and activation in the 500
eV samples. As to the question on why the boron does not continue to activate in the 500
eV samples compared to the 5 KeV samples, this can be explained by considering the
number of interstitials available in the system and the amount of boron diffusion. In
samples where deactivation is occurring there must still be interstitials around with the
amount decreasing as the number of laser pulses increases. The decrease in interstitials
available is evident due to the decrease in diffusion seen in the SIMS as the number of
laser pulses increases prior to the RTA. The decrease in interstitials available also
decreases the amount of boron deactivation when the RTA is given to the samples. The
decrease in deactivation is shown in Figure 6.6 where one pulse plus the RTA causes
80% deactivation and 1000 pulses prior to the RTA only results in 15% deactivation.
This decrease in deactivation is due to the decrease in the number of interstitials available
after the NLA. The deactivated boron in all cases where no loops are present is most
likely due to the formation of BICs during the RTA.
In the 500 eV samples eventually the amount of interstitials is low enough that BICs
cannot be formed during the RTA. The lack of interstitials available to later form BICs
also means there are no interstitials around for sufficient boron diffusion. With little
increase in boron diffusion between 10 to 100 and 100 to 1000 pulses, the amount of
boron activated during the NLA reaches a plateau between 10 to 100 pulses. When the
RTA is applied to these samples, which have fewer interstitials, fewer if any BICs form.
The activation resulting is due to the boron diffusion during the RTA. Recall in
Figure 6.9 that significant dose loss occurs during the RTA. This dose loss requires a
97
significant amount of boron diffusion out of the peak region and into the oxide and
silicon/oxide interface. During this diffusion, the boron becomes substitutional by
interaction with vacancies or the interstitial kickout. The free interstitial can then pair
with another boron causing diffusion and more activation. Anyway, boron in the
presence of a few interstitials results in some boron diffusion which causes more boron
activation than BIC formation.
So, if so few interstitials are available prior to the RTA of these 500 eV samples, what
is the reason for so much diffusion which results in the dose loss and boron activation?
This brings us back to the idea of boron enhanced diffusion (BED). A phenomena
believed to happen in samples implanted with high doses of boron (5e14-1e15/cm2)
[Aga98, Aga99].
BED requires the formation of a silicon boride phase, SiB4. During
the formation of the silicon boride the excess silicon is injected into the nearby region as
silicon interstitials. These interstitials lead to a type of TED which is called BED. If this
silicon boride phase forms during the NLA then the excess interstitials would cause BED
during the NLA and increased diffusion during the RTA due to the extra interstitials.
Since samples receiving one pulse prior to the RTA do in general diffuse more than the
sample receiving just the RTA there is a possibility that SiB4 is forming resulting in
BED. However, all of the diffusion seen during the NLA alone can be explained by the
normal TED expected as defined by the boron-interstitial pair diffusion from Chapter 1.
6.3.4 Mobility and Sheet Resistance
Characterization of actual semiconductor devices requires knowledge of the mobility,
dopant density, sheet resistance and the chemical and electrical junction depth. Plots of
mobility versus concentration and sheet resistance versus junction depth are often
presented and compared to theory. The mobility is generally plotted as a function of the
98
carrier concentration when being discussed in papers [Thu81, Kla90, Kla92, Li79].
Therefore the results for the mobility versus concentration of this work will also be
presented. Figure 6.13 shows how the mobility varies as a function of hole concentration
for the 308 nm and 532 nm experiments. Comparison to previously published data shows
that the values are reasonable [Thu81, Lin81]. In this figure the hole concentration is
determined by using the junction depth measured from SIMS at a boron concentration of
1e18 ion/cm3. Using this chemical junction depth along with the hole density predicted
using Hall effect is really not valid for the gaussian-like boron profiles produced by
implantation, especially when the entire profile is not activated. Instead, the active boron
profiles must be known and those profiles integrated to determine at what depth the given
Hall density given could be obtained. Using this approach, the junction depth would
most likely decrease and the hole concentration increase. Once again, describing a boxlike profile with a concentration over a given depth is more applicable.
Another plot which is very common in industry is the sheet resistance versus junction
depth plot. Figure 6.13 shows plots of the sheet resistance obtained as a function of
junction depth. The top plot shows the results from all of the experiments. The bottom
plot shows the benefit of NLA versus using the convention RTA. Typically the goal is to
continually try to make shallower layers with lower resistivities and produce data points
that appear in the southwest corner of the sheet resistance versus XJ plot. Note that using
the NLA allows for the creation of shallower layers with lower sheet resistances than
conventional annealing techniques.
6.3.5 Mobility, Activation, and Loops
It has been shown that the NLA alone can cause the boron activation and mobility to
increase in the samples with the benefits of increasing the number of laser pulses
99
diminishing as the number of laser pulses increases. Also, the mobility and activation are
not to any great extent affected by the density of visible defects or by the density of the
interstitials in those defects. So it may appear that the mobility and activation are not
affected by the loops. However, recall the TEM microstructure shown in Chapter 3 and 4
after the NLA. The NLA caused the nucleation of a high density of tiny defects which
have been and will be called loops in order to simplify the discussion.
Logically, the presence of this large number of small loops must be affecting the
electrical properties of the layer. The loops act as scattering sites for holes (or electrons).
Increasing the number of scattering sites, decreases the average time between collisions
for the hole which decreases the hole mobility. Scattering from a loop can be due to the
strain fields in the silicon due to the presence of the extra atoms. The scattering can also
be attributed to an effective charge due to dangling bonds at the edges of the loops. This
type of scattering would be similar to ionized impurity scattering.
If it is not the loop density or the interstitial density alone then perhaps the influence
of the size of the loop on the mobility and activation needs to be investigated. Figure
6.15 shows the plots for the hole density and hole mobility versus the average radius of
the loops. The average radius calculated using the following equation:
CI,Loops = π ⋅ R2 ⋅ na ⋅ dLoops
(6.1)
where CI,Loops is the concentration of interstitials in the loops, πR2 is the fractional area of
the loops, na is the atomic density of the <111> plane (1.5e15/cm2), and dLoops is the
density of the loops. As you can see both plots show strong trends. As the average size
of the loops increases, the hole density decreases and the hole mobility increases. Having
the mobility drop as the size drops implies that the smaller loops are more effective at
100
causing hole scattering than the larger loops. A possible explanation is that the small
loops are causing scattering similar to the scattering caused by the neutral impurities in
the layer. Also, the high activation in the presence of the small loops suggests that they
are not very effective at gettering or trapping boron. If these loops were effective at
capturing boron then the hole density would be much lower. Also, note that as the
average size of the loops increases the boron activation decreases. This suggests that the
larger loops are quite effective at trapping and deactivating boron.
6.4 Conclusions
The mobility and activation data for various anneals with the NLA, the RTA, and the
NLA followed by the RTA have been shown. The NLA is found to increase activation
and mobility as the number of laser pulses is increased. This makes it possible to
produce shallower junctions with lower sheet resistances than conventional processing
techniques. Also, the mobility and activation of the layers as a whole are found to vary
significantly as a function of the average number of interstitials in the loops and not as a
function of the total number of interstitials or loops observed in TEM.
Now that a conclusion about the effect of the loops on the mobility and activation has
been reached, an effort will be made to further quantify and model the results. Using the
theory and a model developed over time by Li, Lin, and Linares [Li79, Lin81] for
analyzing the mobility of holes in p-type silicon, a reasonable fit to the data presented can
be made as long as the samples contain large loops or no loops. The model becomes less
accurate as the average number of interstitials in the loops decreases. In Chapter 7 a
mobility model will be presented which extends Li’s model to also include the scattering
from the loops. Using this improved mobility model along with FLOOPS (Florida Object
101
Oriented Process Simulator), the average mobility and sheet resistance of the implanted
layer after various anneal steps can be found.
102
80
Hole Mobility (cm
2/V-s)
70
60
50
40
30
NLA only
20
with RTA
10
0
1
10
100
# of Laser Pulses
2x1015
NLA only
Hole Density (cm
-2
)
with RTA
1x1015
0
1
10
100
# of Laser Pulses
Figure 6.1 The Hall mobility vs. laser energy density is shown following 1040oC, 5 sec
RTA for 5 KeV, 2e15 B+ ions/cm2 samples processed with the 308 nm laser.
% Activation (Hole Density/2e15)
103
100
NLA only
80
with RTA
60
40
20
0
1
10
100
# of Laser Pulses
Figure 6.2 Plot of the percent activation vs. laser energy density following 1040oC, 5 sec
RTA for 5 KeV, 2e15 B+ ions/cm2 samples processed with the 308 nm laser. The active
dose measured with Hall effect is divided by the implanted dose of 2e15 ions/cm2 which
is also the dose measured from SIMS.
104
80
2/V-s)
70
Hole Mobility (cm
60
50
NLA only
40
RTA only
30
20
10
0
1
10
# of Laser Pulses
1x1015
Hole Density (cm
-2
)
NLA only
RTA only
0.5x10 15
0
1
10
# of Laser Pulses
Figure 6.3 Mobility and active dose (hole density) versus number of laser pulses for 1
KeV, 1015/cm2 B for samples receiving just the NLA (NLA only) and those processed
with 1040oC, 5 sec RTA (with RTA).
% Activation (Hole Density/1e15)
105
100
NLA only
80
RTA only
60
40
20
0
1
10
% Activation (Hole Density/7.4e14)
# of Laser Pulses
100
NLA only
80
RTA only
60
40
20
0
1
10
# of Laser Pulses
Figure 6.4 Percent activation versus number of laser pulses for 1 KeV, 1015/cm2 B for
samples receiving just the NLA (NLA only) and those processed with 1040oC, 5 sec RTA
(with RTA). Top picture represents the active dose divided by the dose of the implant,
1e15 ions/cm2 and the bottom picture the active dose divided by the dose determined
from SIMS, 7.4e15 ions/cm2.
106
80
Hole Mobility (cm
2/V-s)
70
60
50
40
30
20
NLA only
RTA only
10
0
1
10
100
1000
# of Laser Pulses
2x1015
NLA only
Hole Density (cm
-2
)
RTA only
1x1015
0
1
10
100
1000
# of Laser Pulses
Figure 6.5 Mobility and hole density versus number of laser pulses of 5 KeV, 2e15 B+
ions/cm2 samples following NLA with the 532 nm laser using a 20 ns pulse length at 100
Hz and/or 1050oC spike anneal.
% Activation (Hole Density/2e15)
107
100
RTA only
NLA only
80
60
40
20
0
1
10
100
1000
# of Laser Pulses
Figure 6.6 Percent activation versus number of laser pulses of 5 KeV, 2e15 B+ ions/cm2
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 Hz
and/or 1050oC spike anneal. The active dose is divided by the dose of the implant, 1e15
ions/cm2.
108
80
NLA only
Hole Mobility (cm
2/V-s)
70
with RTA
60
50
40
30
20
10
0
1
10
100
1000
# of Laser Pulses
10x10 14
with RTA
8x1014
Hole Density (cm
-2
)
NLA only
6x1014
4x1014
2x1014
0
1
10
100
1000
# of Laser Pulses
Figure 6.7 Mobility and hole density versus number of laser pulses of 500 eV, 1e15 B+
ions/cm2 samples following NLA with the 532 nm laser using a 20 ns pulse length at 100
Hz and/or 1050oC spike anneal.
109
100
NLA only
with 1050 oC
spike anneal
% Activation
80
60
40
20
0
1
10
100
1000
% Activation (Hole Density/SIMS Dose)
# of Laser Pulses
100
NLA only
with RTA
80
60
40
20
0
1
10
100
1000
# of Laser Pulses
Figure 6.8 Percent activation versus number of laser pulses of 500 eV, 1e15 B+ ions/cm2
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 Hz
and/or 1050oC spike anneal. The top picture is for the active dose divided by the dose of
the implant, 1e15 ions/cm2, and the bottom picture is for the active dose divided by the
actual SIMS dose.
110
1x1015
After NLA
After NLA + RTA
SIMS Dose (cm
-2
)
0.8x10 15
0.6x10 15
0.4x10 15
0.2x10 15
0
1
10
100
1000
# of Laser Pulses
% Dose Loss During RTA
100
80
60
40
20
0
1
10
100
1000
# of Laser Pulses
Figure 6.9 Dose loss as a result of processing with the NLA and/or the RTA in the
500eV samples processed with the 532 nm laser. The top plot shows the dose measure
from SIMS following each anneal step. The bottom plot shows the percent of dose which
is lost during the RTA.
111
2x1015
500eV 532nm
)
1KeV 308nm
Hole Density (cm
-2
5KeV 308nm
5KeV 532nm
1x1015
0
500
1000
1500
2000
2500
Sheet Resistance (Ohms/sq)
80
Hole Mobility (cm
2/V-s)
70
60
50
500eV, 1e15/cm 2
40
1KeV, 2e15/cm 2
30
5KeV, 2e15/cm 2
5KeV, 2e15/cm 2
20
10
0
0
500
1000
1500
2000
2500
Sheet Resistance (Ohms/sq)
Figure 6.10 Hole density and hole mobility versus sheet resistance measured using Hall
effect. As shown, the change in sheet resistance is not dominated by change s in
mobility, but by the hole density.
112
80
1 KeV 308nm
Hole Mobility (cm
2/V-s)
70
5 KeV 308nm
60
5 KeV 532nm
50
40
30
20
10
0
1x1010
2x1010
3x1010
4x1010
-2
Loop Density (cm )
80
Hole Mobility (cm
2/V-s)
70
60
50
40
30
1 KeV 308nm
20
5KeV 308nm
5KeV 532nm
10
0
0.5x10 14
1x1014
1.5x10 14
2x1014
-2
Interstitial Density (cm )
Figure 6.11 Hole mobility versus loop density and interstitial density are plotted. No
strong trends exist over all of the data.
113
100
500eV 308nm
5KeV 308nm
80
% Activation
5KeV 532nm
60
40
20
0
0.5x10 15
1x1015
1.5x10 15
2x1015
-2
Interstitial Density (cm )
100
1KeV 308nm
5KeV 308nm
80
% Activation
5KeV 532nm
60
40
20
0
1x1010
2x1010
3x1010
-2
Loop Density (cm )
Figure 6.12 Percent activation versus loop density and interstitial density.
114
500eV 532nm
80
1KeV 308nm
5KeV 308nm
Hole Mobility (cm
2/V-s)
70
5KeV 532nm
60
50
40
30
20
10
0
1019
1020
-3
Hole Concentration (cm )
Figure 6.13 Hole mobility versus hole concentration for all processing conditions. The
hole concentration is determined by dividing the hole density by the junction depth
measured at a boron concentration of 1x1018/cm3.
115
Sheet Resistance (Ohms/sq)
2500
500eV 532nm
1KeV 308nm
2000
5KeV 308nm
5KeV 532nm
1500
1000
500
0
500
1000
1500
2000
X Å
J
Sheet Resistance (Ohms/sq)
2500
500eV 532nm NLA only
RTA only
1KeV 308nm NLA only
RTA only
5KeV 308nm NLA only
RTA only
5KeV 532nm NLA only
RTA only
2000
1500
1000
500
0
500
1000
1500
2000
X Å
J
Figure 6.14 Sheet resistance as a function of junction depth for all processes (top) and
NLA alone compared with the conventional RTA (bottom). XJ is measured at a boron
concentration of 1x1018/cm3. The arrows show the benefit of using NLA over
conventional processing anneals.
116
2x1015
Hole Density (cm
-2
)
1KeV 308nm
5KeV 308nm
5KeV 532nm
1x1015
0
200
400
600
Average Radius, R (Å)
80
Hole Mobility (cm
2/V-s)
70
60
50
40
30
1KeV 308nm
5KeV 308nm
5KeV 532nm
20
10
0
200
400
600
Average Radius, R (Å)
Figure 6.15 Plots of the hole density and hole mobility are shown versus the average
radius of the loops. As you can see both plots show strong trends. As the average radius
of the loops increases, the hole density decreases and the hole mobility increases.
CHAPTER 7
MODELING THE MOBILITY
7.1 Introduction
Due to the complexity of integrated circuit processing, it has become increasingly
more difficult and time consuming to develop new processes. The use of process
simulators such as FLOOPS (Florida’s Object Oriented Process Simulator) can help
improve and expedite the development of new processes. Using experimental results to
improve and create models for process simulation is very useful in new technology
development. Knowing the mobility and activation as a result of an implant followed by
anneal steps allows the calculation of the sheet resistance of the layer along with
information on the effects of the defects in the region on device performance. If for
example FLOOPS is used to predict the boron activation and defect clusters as well as
their distribution, this information can be used in combination with an accurate mobility
model to predict the resistivity of a boron implanted layer after processing. The implant
conditions and anneal steps can then be altered until the desired results are obtained.
In the preceding chapters, emphasis is placed on the experimental results for nonmelt
laser annealing of boron-implanted silicon. In Chapter 6, the influence of the physical
properties of the device on the electrical properties is examined. Notably, the mobility is
determined to be influenced by the average radius of the loops. Although a few mobility
models exist for silicon none of these models consider the effect of the damage evolving
during the anneal [Ben83, Ben85, Ben86, Kla90, Kla92, Li79, Lin81]. In this chapter a
theoretical mobility model created and improved upon over time by Li and Linares [Li79.
117
118
Lin81] is examined and compared to the data presented in Chapter 6. The model though
developed for lower doping ranges is shown to accurately predict the mobility when the
number of defects present is small compared to the amount of active boron.
However,
the mobility calculated by the model predicts higher mobilities than shown in
experiments when the defect density is high and the size of those defects small.
Therefore, the model is further improved by adding the effect of the defects on the
mobility. By making the neutral impurity scattering dependent on the interstitial and
defect densities which can be quantified from TEM, a reasonable fit to the data can be
found.
7.2 Li’s and Linares’ Mobility Model
Linares and Li have created a model for analyzing the hole mobility in p-type silicon
which considers the effects of lattice, ionized impurity, and neutral impurity scattering
[Lin81]. They have also taken into account the effects of hole-hole scattering and the
nonparabolic nature of the valence band. Their model has been compared to data for hole
densities varying from 1014 to 1018 holes/cm3. The model is based on the theoretical
model originally developed by Li [Li79]. The model derives the number of neutral and
ionized impurities for a particular boron concentration. The combined mobility for the
lattice and ionized impurity scattering, µLI, is found using the mixed-scattering formula
[Deb54]. The total hole mobility is found by using Mathiesson’s Rules to combine µLI
with the neutral impurity mobility, µN. Using Mathiesson’s Rule here should not add
significant error to the total hole mobility since µN does not affect contributions from µI
(ionized impurity mobility) or µL (lattice mobility). It has been implemented in FLOOPS
to handle a variable boron concentration as an input. The result is a positional dependent
mobility related to the active and neutral concentrations of boron. Therefore, using the
119
SIMS profiles presented in Chapters 3 and 4 and FLOOPS the model can be used to
predict the average mobility and sheet resistance after each anneal step. The results are
presented in Figures 7.1 and 7.2. Recalling the defect microstructure in each sample, it is
shown that the model accurately predicts the results for the mobility and sheet resistance
for samples known or expected to contain only a few defects or large loops.
As shown, the model only appears to fail when the defects in the sample are small and
numerous. Therefore, in order to make the model more accurate for the more heavily
doped boron implanted silicon presented in this work, it is also necessary to take into
account the scattering due to the defects remaining in the sample after the anneal steps
are completed. The defects may be loops, 311s, sub-microscopic interstitial clusters
(SMICs), and/or boron -interstitial clusters (BICs). Knowing more information about the
distribution of the BICs would most likely further improve the model. In Chapter 6 the
mobility is shown to be dependent on the average radius of the loops. If the loops are
considered to be neutral it seems to make sense to see if increasing the number of neutrals
will lead to a better fit to the data.
7.3 The Improved Mobility Model
The influence of the defects on the mobility and the carrier activation is related to the
distribution and size of the defects in the active layer. These defects disrupt the
periodicity of the lattice which decreases the mobility. The high density of defects
formed after the NLA also results in a fairly uniform distribution of the defects across the
layer. This type of distribution itself will decrease the mobility more than the large loops
because the distance between the scattering sites has been dramatically reduced compared
to the defects which would typically evolve. Since these defects have been shown to
evolve into loops, they will once again from hereafter be referred to simply as loops.
120
The reduction in mobility by the loops comes from its ability to scatter a carrier
which is traveling through the lattice. One of the properties of a loop which can cause
scattering is the strain resulting from its presence in the lattice. Since a loop only causes
strain in the lattice around its circumference, the amount of scattering that a loop can do
must be related to its circumference of 2πR where R is the radius of the loop. By
analyzing plan-view TEM images, the average size of the loops can be obtained.
The following method is thus evolved to estimate the scattering cross section of the
loop. The fraction of the area of the loop which causes the scattering is described by 2πR
times L, where L is the width of the strain field which extends around the perimeter of the
loop. The area of the whole loop is πR2. Dividing 2πRL by πR2 produces the fractional
area of the loops which are participating in scattering. Multiplying the number of
interstitials/cm2 trapped in loops by the fractional area of the loop which participates in
scattering gives an estimate of the number of neutral interstitials per cm2 which is
contributing to the scattering. Fitting this dose to a distribution similar to that of the
boron implant produces a concentration of neutrals which can be added to the number of
neutrals used in the mobility model. The model is developed as follows:
DN,Loops = DLoops* 2πRL
(7.1)
where
D I,Loops = πR2 * na* D Loops
(7.2)
is solved for R which is then substituted into Equation 7.2. R is the average radius of the
loops, na is the density of atoms in the <111> plane of 1.5e15/cm2, L is the width of the
scattering region, D Loops is the density of loops observed in the TEM, D I,Loops is the
121
density of interstitials trapped in the loops observed in TEM, and D N, Loops is the density
of neutrals participating in the scattering from the loops. This density of neutrals is then
converted into a concentration versus depth profile with a peak near the projected range
of the implant. These neutrals are finally added to the number of neutrals used in Li’s
model to predict the mobility. The results for simulations of the mobility and sheet
resistances after the NLA, after the RTA, and after the NLA followed by the are
presented in Figures 7.3 through 7.6 for the 5 KeV and 1 KeV data.
An L of 16 Å is
used for all of the data. A full description of the model along with the FLOOPs files can
be found in Appendix B.
As shown in all of the figures, the improved model provided a nice fit to all of the
samples processed with the NLA alone. However, in Figure 1, the mobility is
underestimated in the 5 KeV samples for samples receiving no laser pulses, one laser
pulse, or 10 laser pulses prior to the RTA. Also, the mobility is overestimated in the 1
KeV sample which received only the RTA(Figure 7.5). Although this variation is within
10% of the experimental result value.
Since the model requires input from SIMS and TEM defect quantification, the error in
the data can cause the type of variations seen in the 1 KeV plot. The 5 KeV plot suggests
that further investigation of the model is required. Since the model underestimates the
mobility, it is believed that the error comes from the interpretation of the SIMS data. All
of the former SIMS plots showed some dose loss in the sample following the RTA. The
dose loss from the sample is shown to decrease as the number of laser pulses prior to the
RTA increase. If some dose loss occurred in the 5 KeV samples, the total amount of
boron would be reduced. The number of neutral boron is determined from the total boron
122
dose. The total number of neutrals is found from the number of neutral boron and the
loops. Therefore, any extra boron would cause the number of neutrals to be
overestimated. If the dose of the boron is adjusted for ~7% dose loss in the samples
following the RTA the simulation can be made to fit the experimental results.
Of course, this adjustment brings us to an interesting point. The results are highly
dependent on the SIMS profiles, especially the total dose in those profiles. Using the
model on simulated implanted profiles that do not account for dose loss will add
significant error to the results.
Also, the mobility is found to be dependent on both the neutral impurity scattering and
ionized impurity scattering when the loop density is sufficiently high (such as after
NLA). Typically, dislocation loops may be thought to produce mid-gap states in the band
gap. If these states existed at mid-gap, then their effect o mobility should disappear as
the temperature is decreased and ionized impurity scattering would dominate Hall
mobility versus temperature measurements, however show that from 300K down to 70K
there is no change in the mobility. This suggests that the scattering from the loops is not
due to a mid-gap trap level produced by the loops. The scattering must therefore be
dominated by scattering from the strain field around the loop. This justifies the
assumption of increased neutral scattering due to the presence of loops used in this
model.
7.4 Conclusions
A simple model for the mobility has been presented which results in fairly accurate
fits to samples processed with the NLA. The model suggests that the degradation seen in
the mobility after the NLA can be directly related to the change in microstructure
following the NLA. This change in microstructure results in an increase in the number of
123
neutral scattering sites which is proportional to the circumference of the loops. The
model shown happens to fit the data for the current experiments fairly well. However,
the model of course is quite simple as far a mobility models go. The terms are straight
forward and require user input from physical analysis. A more detailed model would be
based on many more experimental results over a wider range of conditions. This model
would also add the effects of BICs and possibly precipitates on the mobility. Regardless
of what this model does not contain, it does show the dependence of the mobility on
loops. In case you missed it, the high concentrations of small loops increase the carrier
scattering and decrease the mobility.
124
Hole Mobility (cm
2/V-s)
80
70
60
50
40
30
20
after NLA
after RTA
Theory after NLA
Theory after RTA
10
0
1
10
100
1000
# of Laser Pulses
Figure 7.1 This plot compares the theoretical results to the experimental results for the
hole mobility versus number of laser pulses after 532 nm NLA. The 5 KeV, 2e15/cm2
samples are used.
125
Hole Mobility (cm
2/V-s)
80
after NLA
after RTA
Theory after NLA
Theory after RTA
70
60
50
40
30
20
10
0
1
10
# of Laser Pulses
Figure 7.2 This plot compares the theoretical results with the experimental results for the
hole mobility versus number of laser pulses. The 1 KeV, 1e15/cm2 sample results shown
here are processed with the 308 nm laser.
126
Hole Mobility (cm
2/V-s)
80
70
60
50
40
30
after NLA
after RTA
Simulation after NLA
Simulation after RTA
20
10
0
1
10
100
1000
# of Laser Pulses
Figure 7.3 The hole mobility versus the number of laser pulses is shown for the 5 KeV,
2e15/cm2 samples processed with the 532nm laser. The simulation used here included
the dependence of the number of neutrals on the size of the loop.
127
Sheet Resistance (Ohms/sq)
1000
after NLA
after RTA
Simulation after NLA
Simulation after RTA
800
600
400
200
0
1
10
100
1000
# of Laser Pulses
Figure 7.4 The sheet resistance versus the number of laser pulses is shown for the 5
KeV, 2e15/cm2 samples processed with the 532nm laser. The simulation used here
included the dependence of the number of neutrals on the size of the loop.
128
Hole Mobility (cm
2/V-s)
80
70
60
50
40
after NLA
after RTA
Simulation after NLA
Simulation after RTA
30
20
10
0
1
10
# of Laser Pulses
Figure 7.5 The mobility versus the number of laser pulses is shown for the 1 KeV,
1e15/cm2 samples processed with the 308nm laser. The simulation used here included
the dependence of the number of neutrals on the size of the loop.
129
Sheet Resistance (Ohms/sq)
2000
1500
1000
500
after NLA
after RTA
Simulation after NLA
Simulation after RTA
0
1
10
# of Laser Pulses
Figure 7.6 The sheet resistance versus the number of laser pulses is shown for the 1
KeV, 1e15/cm2 samples processed with the 308nm laser. The simulation used here
included the dependence of the number of neutrals on the size of the loop.
CHAPTER 8
SUMMARY, CONCLUSIONS, AND FUTURE WORK
8.1 Summary
In this dissertation, the effects of nonmelt laser annealing on silicon heavily doped
with boron are investigated and analyzed. In FLOOPS, a model using the onedimensional heat flow equation along with surface radiation is implemented to show the
temperature distribution in the wafer during the NLA and during the cooldown. The
boron implanted silicon is investigated after multiple pulses with the NLA. The results
are compared to samples receiving the more conventional RTA. To further understand
how the NLA affects the electrical and structural properties of the implanted layer, the
effects of post-processing on the samples receiving the NLA are also investigated.
Finally, a model for the hole mobility is also implemented in FLOOPS.
In Chapter 1, the motivation and objectives of this work are presented. The ion
implantation process as well as the various electrical and structural analysis techniques
related to this work are reviewed. The physical processes of activation, and annealing,
are discussed. A discussion of the RTA which is currently used for dopant activation in
silicon is presented along with an overview of the laser thermal annealing.
In Chapter 2, the laser-solid interactions are discussed. A model for the temperature
distribution in silicon during the NLA is shown. This model also includes the effect of
surface radiation during the NLA and cooldown which is generally neglected in thermal
estimations. Modeling the temperature allows determination of the total thermal budget
observed in the annealed layer. Understanding the temperature distribution in relation to
130
131
the boron and damage profiles aids in understanding the defect evolution and boron
diffusion during the NLA. Since the temperature distribution is related to the absorption
depth of the laser, it is shown that it is important to make sure the implanted region lies
within this depth. Of course, this is on the assumption that the desire is to have the entire
implanted layer fully annealed. To further investigate the effect of the absorption depth
on the samples, the NLA studies are performed with the 308 nm laser and the 532 nm
laser which have absorption depths of ~70 A and 5000 to 10000 Å respectively. These
absorption depths are for optical measurements made on crystalline silicon.
This brings us to Chapters 3 and 4 which show the results of the 308 nm and 532 nm
laser anneals on the boron distribution and defect evolution. For 5 KeV implants no
diffusion is observed in the boron profiles during the NLA with either laser. For the
shallower 1 KeV and 500 eV implantes, the NLA results in slight diffusion of the boron
profiles during the NLA. Despite the lack of boron diffusion, the NLA alone is also
shown to decrease the sheet resistance in the layers as the number of laser pulses is
increased. Finally, the NLA alone is shown to cause the nucleation of a high-density of
small defects which are visible in TEM.
Chapter 5 uses a longer anneal than the NLA to post-process the samples which
receive the NLA. This longer anneal shows that the defects observed after the NLA
evolve into a high density of small loops. These loops are smaller and higher in density
than in the samples receiving just the RTA or furnace anneal. The NLA is even shown to
cause loops to form in samples which may have otherwise evolved a uniform distribution
of larger loops and 311s. The post-processing also shows that for the lower implant
energies the NLA dramatically if not completely reduces the boron diffusion into the
132
wafer. This lack of diffusion implies that the interstitials available for TED are
drastically reduced as the number of laser pulses increases. The diffusion, interstitial, and
defect information gained here aids in the understanding of the electrical properties
measured in the layers. This brings us to an investigation of the effects of the NLA on
activation and mobility which is done in Chapter 6.
In Chapter 6, the activation and mobility are shown to increase as the number of laser
pulses during the NLA increases. The activation in the samples with the NLA is also
shown to approach 100% in some samples where the conventional RTA only typically
results in 10 to 20% activation in the samples. The NLA is in general shown to reduce
the mobility in the samples which receive the NLA prior to the RTA. It is shown that the
reduction in mobility is not dominated by the individual changes in the interstitials
trapped in the loops or the number of loops visible in TEM. However, this mobility
reduction is shown to be strongly dependent on the average size, or average radius, of the
loops.
The dependence of the mobility on the average radius of the loop is related to the
scattering by the circumference of the loops. This scattering is incorporated into an
existing mobility model. This model shows that the scattering from loops and thus the
mobility reduction can be accounted for by simply increasing the number of neutral
scattering sites in the mobility model. In this model the number of neutrals is determined
from the fractional area of the loops involved in scattering.
8.2 Conclusions
Laser annealing offers considerable advantage compared to conventional spike
annealing. Using NLA with multiple pulses increases the activation and increases the
mobility. This results in a decrease in the sheet resistance with little if any increase in the
133
junction depth. Thus, nonmelt laser annealing alone can be used to produce shallow
junctions with lower resistivity than conventional annealing techniques.
8.3 Suggestions for Future Work
Now that the various results of the NLA has been investigated over a variety of
conditions, more specific studies can be performed to elaborate on some of the details.
For example, a study involving a wider range of implant energies and doses would give
more information into the types of defects evolving in the samples. A large implant and
dose matrix along with post-processing would provide more detailed information on the
activation energies and concentration of the defects evolving from the NLA. Although,
studies must be aggressively geared towards the analysis of shallower, heavily doped
samples. The samples can be at energies less than 1 KeV where the focus would be on
the electrical activation and BIC formation. Perhaps co-implantation of the boron with
germanium of fluorine could be used to produce even shallower junctions with more
abrupt profiles. It would certainly be interesting to investigate the effects of the
germanium and fluorine presence on the mobility and activation.
Another interesting idea might be to combine the nonmelt laser anneal with the the
processes that use laser thermal processing for melting amorphous regions. The first
requirement would be that a laser with a an absorption depth greater than the amorphous
crystalline depth would be used. Then, an NLA would be applied to the amorphized
region prior to the melting laser anneal. Of course, the benefits of multiple pulses should
be studied. The effect of using the NLA would be an attempt to clean up the amorphous
crystalline interface prior to melting and regrowth. This technique should show
improvements over the low-temperature furnace anneals which may not allow for as
much interface repair due to the low temperatures used. A cleaner/smoother interface
134
should reduce the amount of defects in the regrown material. Also, if the laser anneal
heats the damage beyond the amorphous crystalline interface it may also be possible to
remove or at least significantly reduce the end-of-range (EOR) damage. The EOR range
damage results in high leakage currents and may also be a source of interstitials during
post-processing. Having interstitials available during post-processing will increase boron
diffusion and the possibility of boron-interstitial clustering and dopant deactivation.
APPENDIX A
TEMPERATURE SIMULATION DURING NLA USING FLOOPS
The following FLOOPS files are used together to model the temperature distribution
in silicon during the nonmelt laser anneal (NLA): nlaparams.tcl, nlaheating.tcl,
cooldown.tcl, nlaexample.tcl. The files contain all of the variables and constants used for
the simulations presented in the work along with comments. The files are desribed and
presented below. FLOOPS defines the various models required for dopant diffusion in
the TclLib directory. These files must also be modified to account for the nonuniform
temperature distribution, Temp. Although, Dopant.tcl, Potential.tcl, Defect.tcl, and
DefClust.tcl are all used and made dependent on Temp, only Dopant.tcl and Potential.tcl
are provided as examples to show the changes made to the model files.
The file, nlaparams.tcl, shows how the parameter database in FLOOPS can be altered
to accomadate a variable temperature, Temp, for the laser anneal. Using Temp as a
solution variable allows the temperature distribution to be defined by a set of equations
instead of using a constant temperature across the entire gridded region. This of course
requires that the temperature, Temp, be solved for at every time step at each node. Then
all of the other parameters can be found based on the Temp at the desired node. This
model along with boron and defect models can be used to simulate the boron diffusion
and defect evolution in silicon during the NLA.
nlaparams.tcl:
proc nlaArrhenius {pre act} {
set k 8.617383e-05
return "($pre * exp(- 1.0 * $act / ($k * Temp)))"
135
136
}
pdbSetDouble Silicon Int D0.Pf 0.138
pdbSetDouble Silicon Int D0.Ea 1.37
pdbSetDouble Silicon Int Cstr.Pf 3.65652209167e27
pdbSetDouble Silicon Int Cstr.Ea 3.7
pdbSetDouble Silicon Int neg.Pf 5.68
pdbSetDouble Silicon Int neg.Ea 0.48
pdbSetDouble Silicon Int pos.Pf 5.68
pdbSetDouble Silicon Int pos.Ea 0.42
pdbSetDouble Silicon Vac D0.Pf 1.18e-4
pdbSetDouble Silicon Vac D0.Ea 0.1
pdbSetDouble Silicon Vac Cstr.Pf 4.05e+26
pdbSetDouble Silicon Vac Cstr.Ea 3.97
pdbSetDouble Silicon Vac neg.Pf 5.68
pdbSetDouble Silicon Vac neg.Ea 0.145
pdbSetDouble Silicon Vac pos.Pf 5.68
pdbSetDouble Silicon Vac pos.Ea 0.455
pdbSetDouble Silicon Vac dneg.Pf 32.47
pdbSetDouble Silicon Vac dneg.Ea 0.62
pdbSetDouble Silicon Boron Solubility.Pf 7.68e22
pdbSetDouble Silicon Boron Solubility.Ea 0.7086
pdbSetDouble Silicon Boron Int Binding.Pf 8.0e-23
pdbSetDouble Silicon Boron Int Binding.Ea -1.0
pdbSetDouble Silicon Boron Int D0.Pf 0.743
pdbSetDouble Silicon Boron Int D0.Ea 3.56
pdbSetDouble Silicon Boron Int Dp.Pf 0.617
pdbSetDouble Silicon Boron Int Dp.Ea 3.56
pdbSetDouble Silicon Boron Vac Binding.Pf 8.0e-23
pdbSetDouble Silicon Boron Vac Binding.Ea -0.5
pdbSetDouble Silicon Boron Vac D0.Pf 0.186
pdbSetDouble Silicon Boron Vac D0.Ea 3.56
pdbSetDouble Silicon Boron Vac Dp.Pf 0.154
pdbSetDouble Silicon Boron Vac Dp.Ea 3.56
#Alternate z String
#Oxide/Boron
pdbSetString Oxide Boron D0z "([nlaArrhenius 3.16e-4 3.53]"
pdbSetString Oxide Boron Dstarz "([nlaArrhenius 3.16e-4 3.53]"
#Oxide/Boron/Grid
pdbSetString Oxide Boron Grid ScaleVelz "([nlaArrhenius 1.0 2.14])"
#Oxide_Silicon
pdbSetString Oxide_Silicon Boron Segregationz "([nlaArrhenius 1126.0 0.91])"
pdbSetString Oxide_Silicon Boron Transferz "([nlaArrhenius 1.66e-7 0.0])"
pdbSetString Oxide_Silicon Interstitial Scalez "([nlaArrhenius 4.7e-2 2.0])"
pdbSetString Oxide_Silicon Interstitial Injz "([nlaArrhenius 5.56e-3 -0.784])"
pdbSetString Oxide_Silicon Vacancy Scalez "([nlaArrhenius 1.87 2.14])"
#Gas_Oxide
pdbSetString Gas_Oxide Boron Segregationz "([nlaArrhenius 1126.0 0.91])"
pdbSetString Gas_Oxide Boron Transferz "([nlaArrhenius 1.66e-7 0.0])"
pdbSetString Gas_Oxide Interstitial Scalez "([nlaArrhenius 4.7e-2 2.0])"
pdbSetString Gas_Oxide Interstitial Injz "([nlaArrhenius 5.56e-3 -0.784])"
pdbSetString Gas_Oxide Interstitial KinkSitez "([nlaArrhenius 0.186 -3.19])"
pdbSetString Gas_Oxide Interstitial Ksurf2z "([pdbGetString Silicon I D0z] * [pdbGetString Silicon_Ox I
KinkSitez] *[pdbGetString Silicon I Capturez] * [nlaArrhenius 8.0e-23 -1.5])"
pdbSetString Gas_Oxide Vacancy Scalez "([nlaArrhenius 1.87 2.14])"
137
pdbSetString Gas_Oxide Vacancy KinkSitez "([nlaArrhenius 0.186 -3.19])"
pdbSetString Gas_Oxide Vacancy Ksurf2z "([pdbGetString Silicon I D0z] * [pdbGetString Silicon_Ox I
KinkSitez] *[pdbGetString Silicon I Capturez] * [nlaArrhenius 8.0e-23 -1.5])"
#Interface
pdbSetString Interface Boron Segregationz "([nlaArrhenius 1126.0 0.91])"
pdbSetString Interface Boron Transferz "([nlaArrhenius 1.66e-7 0.0])"
pdbSetString Interface Interstitial Scalez "([nlaArrhenius 4.7e-2 2.0])"
pdbSetString Interface Interstitial Injz "([nlaArrhenius 5.56e-3 -0.784])"
pdbSetString Interface Interstitial KinkSitez "([nlaArrhenius 0.186 -3.19])"
pdbSetString Interface Interstitial Ksurf2z "([pdbGetString Silicon I D0z] * [pdbGetString Silicon_Ox I
KinkSitez] * [pdbGetString Silicon I Capturez] * [nlaArrhenius 8.0e-23 -1.5])"
pdbSetString Interface Vacancy Scalez "([nlaArrhenius 1.87 2.14])"
pdbSetString Interface Vacancy KinkSitez "([nlaArrhenius 0.186 -3.19])"
pdbSetString Interface Vacancy Ksurf2z "([pdbGetString Silicon I D0z] * [pdbGetString Si_Ox I
KinkSitez] * [pdbGetString Silicon I Capturez] * [nlaArrhenius 8.0e-23 -0.5])"
#Silicon/311
pdbSetString Silicon 311 Cfz "([nlaArrhenius 6.4e-8 1.4] * [pdbGetString Silicon I Capturez]
*[pdbGetString Silicon I D0z] * [nlaArrhenius 8.0e-23 -1.5] * [nlaArrhenius 8.0e-23 -1.5])"
pdbSetString Silicon 311 Crz "([nlaArrhenius 3.0e15 3.7])"
pdbSetString Silicon 311 Kfz "([nlaArrhenius 2.3e-7 -0.42] * [pdbGetString Silicon I D0z])"
pdbSetString Silicon 311 Krz "([pdbGetString Silicon 311 Kfz] * [nlaArrhenius 4.5e24 2.52])"
#Silicon/Dall
pdbSetString Silicon Dall KRpz "([nlaArrhenius 1.84351726123e-08 1.69727351512])"
#Silicon/Interstitial
pdbSetString Silicon Interstitial D0z "([nlaArrhenius 0.138 1.37])"
pdbSetString Silicon Interstitial Cstarz "([nlaArrhenius [expr 5.0e22*exp(11.2)] 3.7])"
pdbSetString Silicon Interstitial negativez "([nlaArrhenius 5.68 0.48])"
pdbSetString Silicon Interstitial positivez "([nlaArrhenius 5.68 0.42])"
#Silicon/Vacancy
pdbSetString Silicon Vacancy D0z "([nlaArrhenius 1.18e-4 0.1])"
pdbSetString Silicon Vacancy Cstarz "([nlaArrhenius [expr 5.0e22*exp(9.0)] 3.97])"
pdbSetString Silicon Vacancy negativez "([nlaArrhenius 5.68 0.145])"
pdbSetString Silicon Vacancy positivez "([nlaArrhenius 5.68 0.455])"
pdbSetString Silicon Vacancy dnegativez "([nlaArrhenius 32.47 0.62])"
#Gas/Grid/Info
pdbSetString Gas Grid ScaleVelz "([nlaArrhenius 1.0 2.14])"
#Oxide/Grid/Info
pdbSetString Oxide Grid ScaleVelz "([nlaArrhenius 1.0 2.14])"
#Refractory/Grid/Info
pdbSetString Refractory Grid ScaleVelz "([nlaArrhenius 1.0 2.14])"
#Silicon/Boron
pdbSetString Silicon Boron Interstitial D0z "([nlaArrhenius 0.743 3.56])"
pdbSetString Silicon Boron Interstitial Dpz "([nlaArrhenius 0.617 3.56])"
pdbSetString Silicon Boron Vacancy Bindingz "([nlaArrhenius 8.0e-23 -0.5])"
pdbSetString Silicon Boron Vacancy D0z "([nlaArrhenius 0.186 3.56])"
pdbSetString Silicon Boron Vacancy Dpz "([nlaArrhenius 0.154 3.56])"
pdbSetString Silicon Boron Dpz "([pdbGetString Silicon B I Dpz] + [pdbGetString Silicon B V Dpz])"
pdbSetString Silicon Boron D0z "([pdbGetString Silicon B I D0z] + [pdbGetString Silicon B V D0z])"
pdbSetString Silicon Boron Dstarz "([pdbGetString Silicon B I D0z] + [pdbGetString Silicon B I Dpz] +
[pdbGetString Silicon B V D0z] + [pdbGetString Silicon B V Dpz] )"
pdbSetString Silicon Boron Fiz "( ([pdbGetString Silicon B I D0z] + [pdbGetString Silicon B I Dpz]) /
[pdbGetString Silicon B Dstarz] )"
pdbSetString Silicon Boron Solubilityz "([nlaArrhenius 0 0.7086])"
pdbSetString Silicon Boron Solubilityz "([nlaArrhenius 0 0.7086])"
pdbSetString Silicon Boron Solubilityz "([nlaArrhenius 7.68e22 0.7086])"
pdbSetString Silicon Boron Interstitial Bindingz "([nlaArrhenius 8.0e-23 -1.0])"
138
#Silicon/Grid/Info
pdbSetString Silicon Grid ScaleVelz "([nlaArrhenius 1.0 2.14])"
proc nlaDiffLimit {Mat Species Barrier} {
set Dbase 0.0
foreach sol $Species {
set Dbase "($Dbase + ([pdbGetString $Mat $sol D0z]))"
}
set Lspa [pdbGetDouble $Mat LatticeSpacing]
return "[nlaArrhenius "(4.0 * 3.14159 * $Dbase * $Lspa)" $Barrier]"
}
proc nlaConcBind {Mat Entropy Binding} {
set Dens [pdbGetDouble $Mat LatticeDensity]
return "[nlaArrhenius [expr $Dens * exp($Entropy)] $Binding]"
}
proc nlaSurfDiffLimit {Mat Side Sol Barrier} {
set Dbase "([pdbGetString $Side $Sol D0z])"
set Lspa [pdbGetDouble $Side LatticeSpacing]
set Kink [pdbGetDouble $Mat $Sol KinkSite]
return "[nlaArrhenius "(3.14159 * $Dbase * $Lspa * $Kink)" $Barrier]"
}
#set the parameters
pdbSetString Si Potential Permittivityz "11.7"
#from Martin Green's JAP paper
proc nlaGreenBandGap {} {return "(1.2060 - 2.73e-4 * Temp - 1.4e-8 * Temp * Temp)"}
proc nlaSiliconNc {} {
set h 6.62617e-34
set m0 0.91095e-30
set temp [simGetDouble Diffuse tempK]
set mdt "0.1905 * $m0 * 1.2060 / ([nlaGreenBandGap])"
set mdl [expr 0.9163 * $m0]
set md "exp( log( 36.0 * ($mdt) * ($mdt) * $mdl ) / 3.0 )"
set val "2 * 3.141592654 * ($md) * 1.38066e-23 * Temp / ($h * $h)"
return "(($val) * sqrt($val) * 2.0e-6)"
}
pdbSetString Si Potential Ncz "[nlaSiliconNc]"
proc nlaSiliconNv {} {
set h 6.62617e-34
set m0 0.91095e-30
set temp [simGetDouble Diffuse tempK]
set t1 "(0.4435870+Temp* (0.3609528e-2+
Temp*(0.1173515e3+Temp*(0.1263218e5+Temp*0.3025581e-8))))"
set t2 "(1.0+Temp*(0.4683382e-2+Temp*(0.2286895e-+Temp*(0.7469271e6+Temp*0.1727481e8))))"
set md "exp( log($t1/$t2) * 2.0/3.0) * $m0 "
set val "(2 * 3.141592654 * ($md) * 1.38066e-23 * Temp / ($h * $h))"
return "($val * sqrt($val) * 2.0e-6)" }
139
pdbSetString Si Potential Nvz "[nlaSiliconNv]"
pdbSetString Vtiz "(1.0/(8.617383e-05*Temp))"
pdbSetString Si Potential niz "sqrt(([pdbGetString Si Potential Ncz])*([pdbGetString Si Potential Nvz])) *
exp( -0.5 * ([nlaGreenBandGap]) * ([pdbGetString Vtiz]))"
set k 8.617383e-05
pdbSetString Oxide_Silicon Interstitial thetaz "0.0"
pdbSetString Oxide_Silicon Interstitial Kratz "0.0"
pdbSetString Oxide_Silicon I2 Ksurfz "([nlaSurfDiffLimit Oxide_Silicon Silicon I2 0.0]])"
pdbSetString Oxide_Silicon Interstitial Ksurfz "([nlaSurfDiffLimit Oxide_Silicon Si Int 0.0])"
pdbSetString Oxide_Silicon Interstitial Ktrapz "(10.0*[nlaSurfDiffLimit Oxide_Silicon Si Int 0.0])"
pdbSetString Oxide_Silicon V2 Ksurfz "([nlaSurfDiffLimit Oxide_Silicon Silicon V2 0.0])"
pdbSetString Oxide_Silicon Vacancy Ksurfz "([nlaSurfDiffLimit Oxide_Silicon Si Vac 0.0])"
pdbSetString Oxide_Silicon Vacancy Ktrapz "(10.0*[nlaSurfDiffLimit Oxide_Silicon Si Vac 0.0])"
pdbSetString Silicon C311 BindIz "([nlaConcBind Silicon 4.8 2.275])"
pdbSetString Silicon I2 Bindz "([nlaConcBind Si 0.0 2.0])"
pdbSetString Silicon I4 Bindz "[nlaConcBind Si 0.0 0.8]"
pdbSetString Silicon I6 Bindz "[nlaConcBind Si 0.0 0.8]"
pdbSetString Silicon Smic Bindz "[nlaConcBind Silicon 11.9 2.1]"
pdbSetString Silicon V2 Bindz "[nlaConcBind Si 0.0 2.5]"
pdbSetString Silicon C311 KnI2z "[nlaDiffLimit Silicon I2 1.1]"
pdbSetString Silicon C311 KfI2z "[nlaDiffLimit Silicon I2 0.0]"
pdbSetString Silicon C311 KfIz "[nlaDiffLimit Silicon Int 0.1]"
pdbSetString Silicon C311 KfV2z "[nlaDiffLimit Silicon V2 0.0]"
pdbSetString Silicon C311 KfVz "[nlaDiffLimit Silicon Vac 0.0]"
pdbSetString Silicon I2 Kforwardz "[nlaDiffLimit Si Int 0.0]"
pdbSetString Silicon I2 KRecombz "[nlaDiffLimit Si {I2 Vac} 0.0]"
pdbSetString Silicon I2 KBiMolez "(0.5*[nlaDiffLimit Si {V2 I2} 0.0])"
pdbSetString Silicon I4 Kforwardz "(4.0 * [nlaDiffLimit Si I2 0.0])"
pdbSetString Silicon I4 KRecombz "(4.0*[nlaDiffLimit Si V2 0.0])"
pdbSetString Silicon I6 Kforwardz "(6.0 * [nlaDiffLimit Si I2 0.0])"
pdbSetString Silicon I6 KRecombz "(6.0*[nlaDiffLimit Si V2 0.0])"
pdbSetString Silicon Smic KfIz "[nlaDiffLimit Silicon Int 0.0]"
pdbSetString Silicon V2 Kforwardz "[nlaDiffLimit Si Vac 0.3]"
pdbSetString Silicon V2 KRecombz "[nlaDiffLimit Si {V2 Int} 0.0]"
pdbSetString Silicon V2 KBiMolez "(0.5*[nlaDiffLimit Si {V2 I2} 0.0])"
pdbSetString Silicon Boron Interstitial Kratez "[nlaDiffLimit Silicon Int 0.0]"
pdbSetString Silicon Boron Vacancy Kratez "[nlaDiffLimit Silicon Vac 0.0]"
#pdbSetString Silicon Phosphorus Interstitial Krate "[nlaDiffLimit Si Int 0.0]"
proc nlaInitDefect {} {
# SetTemp
#turn on the defects
pdbSetSwitch Si I DiffModel Numeric
pdbSetSwitch Si V DiffModel Numeric
solution name = Int solve !damp !negative
solution name = Vac solve !damp !negative
sel z= [pdbGetString Si I Cstarz] name=Int store
sel z= [pdbGetString Si V Cstarz] name=Vac store }
140
#create cluster solution variables
solution add name=I2 ifpresent = "Int I2" !damp !negative
pdbSetString Si I2 EquationProc 2Defect
pdbSetString Si I2 InitProc DefectInit
pdbSetString Ox_Si I2 EquationProc 2Bound
solution add name=C311 ifpresent = "Int I2 C311" !damp !negative
solution add name=D311 ifpresent = "Int I2 D311" !damp !negative
solution add name=Smic ifpresent = "Int I2 Smic" !damp !negative
pdbSetString Si C311 EquationProc 311Eqn
pdbSetString Si C311 InitProc C311Init
solution add name=V2 ifpresent = "V2 Vac" !negative
pdbSetString Si V2 EquationProc 2Defect
pdbSetString Si V2 InitProc DefectInit
pdbSetString Ox_Si V2 EquationProc 2Bound
proc nlaInitCluster {} {
solution add name=I2 solve !damp !negative
solution add name=V2 solve !damp !negative
sel z = [pdbGetString Si I2 Cstarz] name = I2 store
sel z = [pdbGetString Si I4 Cstarz] name = I4 store
sel z = [pdbGetString Si V2 Cstarz] name = V2 store
sel z = 1.0 name = D311 store
}
The file, nlaheating.tcl sets up the parameters to determine how the temperature,
Temp, will vary during the laser anneal.
nlaheating.tcl:
#the parameters are all functions of
#temperature. the analytical fits to data
#are given. if used you will have trouble
#converging when boron and defects added. so,
#use the average values which are close to
#room temp values.
#density kg/cm3
set p 2.33
#thermal conductivity W/cm-K
#Km meters... Kcm cm... K(Temp)
#set Km "2.99e4/(Temp-99.0)"
#set Kcm "$Km*1.0e-2"
set K 0.6
#thermal capacity J/kg-K
#Cp also a function of Temp...
#set Cp "(1.4743+5.689e-4*Temp)*1.0e6/$p"
set Cp 0.7
#latent heat... if phase change... J/kg
141
#set deltah 1.4e6
#absorption coefficient, 1/cm
set a1 4.4e4
set a2 [expr $a1/1.0e4]
#1/absorption depth is temp dependent
#this will work for temp only but never
#converges with boron and defects...
#set a1 0.8e4
#set a1 "$a1*exp((Temp-300.0)/430.0)"
#set a2 "$a1/1.0e4"
#you can use the variable R too, but
#no significant change... if you use
#R(Temp) then you need to adjust a1
#set R "0.5+5.0e-5*Temp"
set R 0.5
#laser intensity W/cm2
set J 0.35
set plength 20.0e-9
set I [expr $J/$plength]
pdbSetString Si Temp Equation "(-$K*grad(Temp)-$I*(1.0-$R)*$a1*exp(-$a2*x)+ddt($p*$Cp*Temp))"
sel z=300 name=Temp store
The file, cooldown.tcl, sets up the parameters to determine how the temperature,
Temp, will vary during the cooldown after the laser is turned off.
cooldown.tcl:
#sigma is the stefan-boltzmann constant (W*cm-2*K-4) convert
#to microns...
#set sigma [expr (5.67e-12)*1.0e-8]
set sigma 5.67e-12
#need to know volume of piece/wafer being cooled
#set volume [expr 1.0*1.0e12]
set volume 0.001
#need to know area in contact with air
#set area [expr 1.0/1.0e-8]
set area 1.0
#emissivity of silicon (black body=max of 1)
set e 0.1
#set K 0.76
set pC 2.33
set cpC 0.9
pdbSetString Oxide_Silicon Temp Equation_Silicon "$e * $sigma * $area / ($volume * $pC *$cpC) *
Temp_Silicon^4.0"
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pdbSetString Silicon Temp Equation "- $pC * $cpC * ddt(Temp) + $K * grad(Temp)
The file simplecooldown.tcl is included which shows an equation for Temp used to aid
in convergence. The equation is a simpler analytical fit found to the define the cooldown.
This file will speed up the simulation.
simplecooldown.tcl:
#sigma is the stefan-boltzmann constant (W*cm-2*K-4)
set sigma 5.67e-12
#need to know volume of piece/wafer being cooled
set volume 0.001
#need to know area in contact with air
set area 2.0
#emissivity of silicon (black body=max of 1)
#silicon is a gray body include(Temp) if you want.
set e 0.4
#set in heatingparams.tcl
set p 2.33
set Cp 0.7
set K 0.6
pdbSetString Silicon Temp Equation "$p * $Cp * ddt(Temp) - $K * grad(Temp)"
pdbSetString Oxide_Silicon Temp Equation_Silicon "-1.0e-2*Temp^2"
The file, nlaexample.tcl, reads in nlaparams.tcl to set up the required parameters for
boron and defect diffusion. A grid is generated and boron implanted. Temp is added to
the list of solution variables. The initial interstitial profile is assumed to be equal to the
boron as-implanted profile. The file is set up for 1000 pulses at 20 ns/pulse with a
frequency of 100 Hz. During the NLA the Temp equation is set by sourcing the file
nlaheating.tcl and an initial temperature of 300K. After the NLA the silicon is defined to
cool according to the parameters defined in cooldown.tcl (or simplecooldown.tcl).
nlaexample.tcl:
math diffuse dim=1 umf none triplet
source ~ske/source/nlaparams.tcl
source ~ske/myfloops/TclLib/Dopant.tcl
143
source ~ske/myfloops/TclLib/Potential.tcl
source ~ske/myfloops/TclLib/Defect.tcl
source ~ske/myfloops/TclLib/DefClust.tcl
pdbSetString Si Boron InitProc InitDopant
solution name=Potential damp
pdbSetSwitch Si I DiffModel Numeric
pdbSetSwitch Si V DiffModel Numeric
solution name = Int solve !damp !negative
solution name = Vac solve !damp !negative
pdbSetDouble Silicon Int Dp [pdbDelayDouble Si Int D0]
pdbSetDouble Ox_Si Int Ksurf {[Arrhenius 1.95 2.5]}
line x loc=-0.01 tag=oxi spac=0.01
line x loc=0.0 tag=top spac=0.001
line x loc=0.4 spac=0.001
line x loc=1.0 tag=bot spac=0.05
#line x loc=50.0 spac=1.0
#line x loc=100.0 tag=bot spac=5.0
region silicon xlo=top xhi=bot
region oxide xlo=oxi xhi=top
init
implant dose=2.0e15 energy=5 boron ang=7
set roomtemp 25
sel z=($roomtemp+273.0) name=Temp store
SetTemp $roomtemp
InitDefect $roomtemp
pdbSetSwitch Si Boron DiffModel React
sel z=Boron name=Int store
set CompGraph [CreateGraphWindow]
sel z=log10(Boron)
CreateLine $CompGraph AsImplanted [slice silicon]
set pulsemin [expr 20e-9/60.0]
set freq [expr 100.0*60.0]
plot.xy min = {0 0} max = {1000 1e16}
global ct
set ct [open 5KeV2e15PairDosedata w]
for {set i 1} {$i <= 1000} {incr i} {
sel z=300.0 name=Temp store
source nlaheating.tcl
diffuse temp=$roomtemp time=$pulsemin init=1e-12
source cooldown.tcl
diffuse temp=$roomtemp time=[expr 1.9e-4/60.0-$pulsemin] init=1e-12
pdbSetString Silicon Temp Equation "Temp"
sel z=300 name=Temp store
144
diffuse temp=$roomtemp time=[expr 1.0/$freq-1.9e-4/60.0-$pulsemin] init=1e-12
sel z=Int
set IntDose [FindDose]
sel z=Boron+BoronInt+BoronVac
set TotalBoronDose [FindDose]
sel z=BoronActive
set BoronActiveDose [FindDose]
point.xy x = $i y = $IntDose name = IntDose
point.xy x = $i y = $TotalBoronDose name = TotalBoronDose
point.xy x = $i y = $BoronActiveDose name = BoronActiveDose
puts -nonewline $ct $i
puts -nonewline $ct " "
puts -nonewline $ct $IntDose
puts -nonewline $ct " "
puts -nonewline $ct $TotalBoronDose
puts -nonewline $ct " "
puts -nonewline $ct $BoronActiveDose
puts -nonewline $ct " "
puts $ct " "
flush $ct
}
sel z=log10(Boron)
CreateLine $CompGraph Pair1000 [slice silicon]
Dopant.tcl:
proc InitDopant {Mat Sol} {
set pdbMat [pdbName $Mat]
set model [pdbGetSwitch $pdbMat $Sol DiffModel]
#if we have the react model, we need to set up solutions
if {$model == 3} {
#get a list of defects we react with
set ld [pdbGetString $pdbMat $Sol Defects]
foreach d $ld {
solution add name = ${Sol}${d} solve !damp !negative
}
puts "Reaction Model for $Sol"
#else we need to make sure things are clear!
} else {
#get a list of defects we react with
set ld [pdbGetString $pdbMat $Sol Defects]
foreach d $ld {
solution name = ${Sol}${d} nosolve !damp !negative
}
}
}
proc DopantBulk { Mat Sol } {
145
set k 8.617383e-05
set pdbMat [pdbName $Mat]
puts "DopantBulk1"
#work with the active model - create DopantActive...
set ActModel [pdbGetSwitch $pdbMat $Sol ActiveModel]
set ActName ${Sol}Active
if {$ActModel == 0} {
term name = $ActName add eqn = $Sol $Mat
} elseif {$ActModel == 1} {
set ssPf [pdbGetDouble $pdbMat $Sol Solubility.Pf]
set ssEa [pdbGetDouble $pdbMat $Sol Solubility.Ea]
set ss "($ssPf * exp(- 1.0 * $ssEa / ($k * Temp)))"
term name = $ActName add eqn = "$ss * $Sol / ($ss + $Sol)" $Mat
} else {
#need to add dynamic precipitation here!
set ssPf [pdbGetDouble $pdbMat $Sol Solubility.Pf]
set ssEa [pdbGetDouble $pdbMat $Sol Solubility.Ea]
set ss "($ssPf * exp(- 1.0 * $ssEa / ($k * Temp)))"
term name = $ActName add eqn = "$ss * $Sol / ($ss + $Sol)" $Mat
}
puts "DopantBulk2"
set model [pdbGetSwitch $pdbMat $Sol DiffModel]
set ChgName 0
if {$model == 0} {
set ChgName [DopantConstant $Mat $Sol]
} elseif {$model == 1} {
set ChgName [DopantFermi $Mat $Sol]
} elseif {$model == 2} {
set ChgName [DopantPair $Mat $Sol]
} elseif {$model == 3} {
puts "calling DopantReact"
set ChgName [DopantReact $Mat $Sol]
}
puts "DopantBulk3"
#set up charged species in potential equation
set chgtype [pdbGetSwitch $pdbMat $Sol Charge]
set chg [term name=Charge print $Mat]
if {[lsearch $chg $ChgName] == -1} {
#acceptor
if {$chgtype == 1} {
term name = Charge add eqn = "$chg - $ChgName" $Mat
#donor
} elseif {$chgtype == 2} {
term name = Charge add eqn = "$chg + $ChgName" $Mat
}
#neutrals
} elseif {$chgtype == 0} {}
}
146
proc DopantConstant { Mat Sol } {
set k 8.617383e-05
set pdbMat [pdbName $Mat]
set D0IPf [pdbGetDouble $pdbMat $Sol I D0.Pf]
set D0IEa [pdbGetDouble $pdbMat $Sol I D0.Ea]
set diff0I "($D0IPf * exp(- 1.0 * $D0IEa / ($k * Temp)))"
set D0VPf [pdbGetDouble $pdbMat $Sol V D0.Pf]
set D0VEa [pdbGetDouble $pdbMat $Sol V D0.Ea]
set diff0V "($D0VPf * exp(- 1.0 * $D0VEa / ($k * Temp)))"
set DpIPf [pdbGetDouble $pdbMat $Sol I Dp.Pf]
set DpIEa [pdbGetDouble $pdbMat $Sol I Dp.Ea]
set diffpI "($DpIPf * exp(- 1.0 * $DpIEa / ($k * Temp)))"
set DpVPf [pdbGetDouble $pdbMat $Sol V Dp.Pf]
set DpVEa [pdbGetDouble $pdbMat $Sol V Dp.Ea]
set diffpV "($DpVPf * exp(- 1.0 * $DpVEa / ($k * Temp)))"
set diff "($diff0I + $diff0V + $diffpI + $diffpV)"
set ActName ${Sol}Active
puts "DopantConstant"
pdbSetString $pdbMat $Sol Equation "ddt($Sol) - $diff * grad( $ActName )"
return $ActName
}
proc DopantFermi { Mat Sol } {
set pdbMat [pdbName $Mat]
set k 8.617383e-05
#build the diffusivity
set difnam Diff$Sol
puts "DopantFermi1"
#build the diffusivity term
# set dif [pdbGetDouble $Mat $Sol D0]
set D0IPf [pdbGetDouble $pdbMat $Sol I D0.Pf]
set D0IEa [pdbGetDouble $pdbMat $Sol I D0.Ea]
set diff0I "($D0IPf * exp(- 1.0 * $D0IEa / ($k * Temp)))"
set D0VPf [pdbGetDouble $pdbMat $Sol V D0.Pf]
set D0VEa [pdbGetDouble $pdbMat $Sol V D0.Ea]
set diff0V "($D0VPf * exp(- 1.0 * $D0VEa / ($k * Temp)))"
set dif "($diff0I + $diff0V)"
puts "DopantFermi2"
if {[pdbIsAvailable $Mat $Sol Dn]} {
set dif "$dif + [pdbGetDouble $Mat $Sol Dn] * Noni"
}
if {[pdbIsAvailable $Mat $Sol Dnn]} {
set dif "$dif + [pdbGetDouble $Mat $Sol Dnn] * Noni^2"
}
if {[pdbIsAvailable $Mat $Sol Dp]} {
#
set dif "$dif + [pdbGetDouble $Mat $Sol Dp] * Poni"
set DpIPf [pdbGetDouble $pdbMat $Sol I Dp.Pf]
set DpIEa [pdbGetDouble $pdbMat $Sol I Dp.Ea]
set diffpI "($DpIPf * exp(- 1.0 * $DpIEa / ($k * Temp)))"
set DpVPf [pdbGetDouble $pdbMat $Sol V Dp.Pf]
set DpVEa [pdbGetDouble $pdbMat $Sol V Dp.Ea]
147
set diffpV "($DpVPf * exp(- 1.0 * $DpVEa / ($k * Temp)))"
set dif2 "($diffpI + $diffpV]
# set dif "$dif + [pdbGetDouble $Mat $Sol Dp] * Poni"
set dif "$dif + $dif2 * Poni"
}
if {[pdbIsAvailable $Mat $Sol Dpp]} {
set dif "$dif + [pdbGetDouble $Mat $Sol Dpp] * Poni^2"
}
puts "Ferimnear3"
# set difnam "$dif"
term name = $difnam add eqn = "$dif" $Mat
puts "DopantFermi3"
set ActName ${Sol}Active
set eqn "ddt($Sol) - $difnam * grad( $ActName )"
set chgtype [pdbGetSwitch $pdbMat $Sol Charge]
if {$chgtype == 1} {
#
set difnam "$dif / Poni"
term name = $difnam add eqn = "($dif) / Poni" $Mat
set eqn "ddt($Sol) - $difnam * grad( $ActName * Poni )"
} elseif {$chgtype == 2} {
#
set difnam "$dif / Noni"
term name = $difnam add eqn = "($dif) / Noni" $Mat
set eqn "ddt($Sol) - $difnam * grad( $ActName * Noni )"
}
pdbSetString $pdbMat $Sol Equation $eqn
return $ActName
}
proc DopantDefectPair { Mat Sol Def } {
set k 8.617383e-05
set pdbMat [pdbName $Mat]
puts "DopantDefectPair $Mat $Sol $Def"
#buld the diffusivity
set difnam Diff${Sol}${Def}
#
#build the diffusivity term
set dif [pdbGetDouble $Mat $Sol $Def D0]
set D0Pf [pdbGetDouble $pdbMat $Sol $Def D0.Pf]
set D0Ea [pdbGetDouble $pdbMat $Sol $Def D0.Ea]
set dif "($D0Pf * exp(- 1.0 * $D0Ea / ($k * Temp)))"
if {[pdbIsAvailable $Mat $Sol $Def Dn]} {
set dif "$dif + [pdbGetDouble $Mat $Sol $Def Dn] * Noni"
set DnPf [pdbGetDouble $pdbMat $Sol $Def Dn.Pf]
set DnEa [pdbGetDouble $pdbMat $Sol $Def Dn.Ea]
set dif "($dif + ($DnPf * exp(- 1.0 * $dnEa / ($k * Temp))) * Noni)"
}
if {[pdbIsAvailable $Mat $Sol Dnn]} {
#
set dif "$dif + [pdbGetDouble $Mat $Sol $Def Dnn] * Noni^2"
set DnnPf [pdbGetDouble $pdbMat $Sol $Def Dnn.Pf]
set DnnEa [pdbGetDouble $pdbMat $Sol $Def Dnn.Ea]
#
148
set dif "($dif + ($DnnPf * exp(- 1.0 * $DnnEa / ($k * Temp))) * Noni^2)"
}
if {[pdbIsAvailable $Mat $Sol Dp]} {
#
set dif "$dif + [pdbGetDouble $Mat $Sol $Def Dp] * Poni"
set DpPf [pdbGetDouble $pdbMat $Sol $Def Dp.Pf]
set DpEa [pdbGetDouble $pdbMat $Sol $Def Dp.Ea]
set dif "($dif + ($DpPf * exp(- 1.0 * $DpEa / ($k * Temp))) * Poni)"
}
if {[pdbIsAvailable $Mat $Sol Dpp]} {
#
set dif "$dif + [pdbGetDouble $Mat $Sol $Def Dpp] * Poni^2"
set DppPf [pdbGetDouble $pdbMat $Sol $Def Dpp.Pf]
set DppEa [pdbGetDouble $pdbMat $Sol $Def Dpp.Ea]
set dif "($dif + ($DppPf * exp(- 1.0 * $DppEa / ($k * Temp))) * Poni^2)"
}
set SubName ${Sol}Sub
set chgtype [pdbGetSwitch $Mat $Sol Charge]
set chg 1.0
if {$chgtype == 1} {
set chg Poni
} elseif {$chgtype == 2} {
set chg Noni
}
puts $dif
term name = $difnam add eqn = "( $dif ) / $chg" $Mat
set eqn "$difnam * grad( $SubName * Scale${Def} * $chg )"
term name = Flux${Sol}${Def} add eqn = $eqn $Mat
puts "$Sol $eqn"
set de [pdbGetString $Mat $Sol Equation]
pdbSetString $Mat $Sol Equation "$de - Flux${Sol}${Def}"
set de [pdbGetString $Mat $Def Equation]
# set bind [pdbGetDouble $Mat $Sol $Def Binding]
set BinPf [pdbGetDouble $pdbMat $Sol $Def Binding.Pf]
set BinEa [pdbGetDouble $pdbMat $Sol $Def Binding.Ea]
set bind "($BinPf * exp(- 1.0 * $BinEa / ($k * Temp)))"
pdbSetString $Mat $Def Equation "$de + ddt($bind * $SubName * $Def) - Flux${Sol}${Def}"
}
proc DopantPair { Mat Sol } {
set k 8.617383e-05
set pdbMat [pdbName $Mat]
#get all of the defects we are working with
set ld [pdbGetString $pdbMat $Sol Defects]
#build an expression for the substitutional dopant
set ActName ${Sol}Active
set den 1.0
foreach d $ld {
#
set den "$den + $d * [pdbGetDouble $pdbMat $Sol $d Binding]"
set BindingPf [pdbGetDouble $pdbMat $Sol $d Binding.Pf]
set BindingEa [pdbGetDouble $pdbMat $Sol $d Binding.Ea]
set Bindingd "($BindingPf * exp(- 1.0 * $BindingEa / ($k * Temp)))"
set den "$den + $d * $Bindingd"
}
149
term name = ${Sol}Sub add eqn = "$ActName / ( $den )" $Mat
#create the basic equation and then add
pdbSetString $pdbMat $Sol Equation "ddt( $Sol )"
#for each dopant defect pair, build the flux
foreach d $ld {
DopantDefectPair $pdbMat $Sol $d
}
puts [pdbGetString $pdbMat $Sol Equation]
return ${Sol}Sub
}
proc Segregation { Mat Sol } {
set k 8.617383e-05
set pdbMat [pdbName $Mat]
#get the names of the sides
set s1 [FirstMat $pdbMat]
set s2 [SecondMat $pdbMat]
set ss1 [pdbIsAvailable $s1 $Sol DiffModel]
set ss2 [pdbIsAvailable $s2 $Sol DiffModel]
if { $ss1 && $ss2 } {
puts "$pdbMat $Sol"
set seg [pdbGetString $pdbMat $Sol Segregationz]
set trn [pdbGetString $pdbMat $Sol Transferz]
puts "$seg $trn"
set sm1 ${Sol}_$s1
set sm2 ${Sol}_$s2
set eq "$trn * ($sm1 - $sm2 / $seg)"
pdbSetString $pdbMat $Sol Equation_$s1 "- $eq"
pdbSetString $pdbMat $Sol Equation_$s2 "$eq"
}
}
proc DopantDefectReact { Mat Sol Def } {
set k 8.617383e-05
puts "DopantDefectReact $Mat $Sol $Def"
set S ${Sol}${Def}
set pdbMat $Mat
#assume the dopant-defect diffusivity is constant
set BinPf [pdbGetDouble $pdbMat $Sol $Def Binding.Pf]
set BinEa [pdbGetDouble $pdbMat $Sol $Def Binding.Ea]
set B "($BinPf * exp(- 1.0 * $BinEa / ($k * Temp)))"
set CsPf [pdbGetDouble $pdbMat $Def Cstr.Pf]
150
set CsEa [pdbGetDouble $pdbMat $Def Cstr.Ea]
set Cs "($CsPf * exp(- 1.0 * $CsEa / ($k * Temp)))"
set D0Pf [pdbGetDouble $pdbMat $Sol $Def D0.Pf]
set D0Ea [pdbGetDouble $pdbMat $Sol $Def D0.Ea]
set D0 "($D0Pf * exp(- 1.0 * $D0Ea / ($k * Temp)))"
set dax "$D0 / ($B * $Cs)"
puts "predax"
puts $dax
#
#
#
#
#build the effective charge state dependent binding
set Bind 1
if {[pdbIsAvailable $Mat $Sol $Def Dn]} {
set Bind "$Bind + [pdbGetDouble $Mat $Sol $Def Dn] * Noni / $D0"
set DnPf [pdbGetDouble $pdbMat $Sol $Def Dn.Pf]
set DnEa [pdbGetDouble $pdbMat $Sol $Def Dn.Ea]
set Dn "($DnPf * exp(- 1.0 * $DnEa / ($k * Temp)))"
set Bind "$Bind + $Dn * Noni / $D0"
}
if {[pdbIsAvailable $Mat $Sol Dnn]} {
set Bind "$Bind + [pdbGetDouble $Mat $Sol $Def Dnn] * Noni^2 / $D0"
set DnnPf [pdbGetDouble $pdbMat $Sol $Def Dnn.Pf]
set DnnEa [pdbGetDouble $pdbMat $Sol $Def Dnn.Ea]
set Dnn "($DnnPf * exp(- 1.0 * $DnnEa / ($k * Temp)))"
set Bind "$Bind + $Dnn * Noni^2 / $D0"
}
if {[pdbIsAvailable $Mat $Sol Dp]} {
set Bind "$Bind + [pdbGetDouble $Mat $Sol $Def Dp] * Poni / $D0"
set DpPf [pdbGetDouble $pdbMat $Sol $Def Dp.Pf]
set DpEa [pdbGetDouble $pdbMat $Sol $Def Dp.Ea]
set Dp "($DpPf * exp(+ 1.0 * $DpEa / ($k * Temp)))"
set Bind "$Bind + $Dp * Poni / $D0"
}
if {[pdbIsAvailable $Mat $Sol Dpp]} {
set Bind "$Bind + [pdbGetDouble $Mat $Sol $Def Dpp] * Poni^2 / $D0"
set DppPf [pdbGetDouble $pdbMat $Sol $Def Dpp.Pf]
set DppEa [pdbGetDouble $pdbMat $Sol $Def Dpp.Ea]
set Dpp "($DppPf * exp(- 1.0 * $DppEa / ($k * Temp)))"
set Bind "$Bind + $Dpp * Poni^2 / $D0"
}
set SubName ${Sol}Sub
set chgtype [pdbGetSwitch $Mat $Sol Charge]
set chg 1.0
if {$chgtype == 1} {
set chg Poni
} elseif {$chgtype == 2} {
set chg Noni
}
puts $dax
set flux "$dax * grad( $S * $chg ) / $chg"
puts $flux
puts $Bind
#build the reaction
151
set K [pdbGetString $Mat $Sol $Def Kratez]
term name = React$S add eqn = "$K * (${Sol}Sub * $Def - ${Sol}${Def} / ($B * ($Bind)))" $Mat
set de [pdbGetString $Mat $Sol Equation]
pdbSetString $Mat $Sol Equation "$de + React$S"
set de [pdbGetString $Mat $Def Equation]
pdbSetString $Mat $Def Equation "$de + React$S"
pdbSetString $Mat ${Sol}${Def} Equation "ddt($S) - $flux - React$S"
}
proc DopantReact { Mat Sol } {
set k 8.617383e-05
set pdbMat [pdbName $Mat]
#get all of the defects we are working with
set ld [pdbGetString $pdbMat $Sol Defects]
#see if we have created a substitutional solution variable
set ActName ${Sol}Active
set den $ActName
foreach d $ld {
set den "$den - ${Sol}${d}"
}
term name = ${Sol}Sub add eqn = "$den" $Mat
puts "Substitutional is [term name = ${Sol}Sub $Mat print]"
#create the basic equation and then add to it
pdbSetString $pdbMat $Sol Equation "ddt( $Sol )"
puts [pdbGetString $pdbMat $Sol Equation]
#for each dopant defect pair, build the flux
foreach d $ld {
puts "calling DopantDefectReact"
DopantDefectReact $pdbMat $Sol $d
puts "return from DopantDefectReact"
}
puts "you made it here"
puts [pdbGetString $pdbMat $Sol Equation]
return ${Sol}Sub
}
Potential.tcl:
proc PotentialEqns { Mat Sol } {
set pdbMat [pdbName $Mat]
set Vti "(1.0/(8.617383e-05*Temp))"
set terms [term list]
if {[lsearch $terms Charge] == -1} {
term name = Charge add eqn = 0.0 $Mat
}
152
set Poiss 0
if {[pdbIsAvailable $pdbMat $Sol Poisson]} {
if {[pdbGetBoolean $pdbMat $Sol Poisson]} {set Poiss 1}
}
set ni "([pdbGetString $pdbMat $Sol niz])"
if {! $Poiss} {
set neq "(0.5*(Charge+sqrt(Charge*Charge+4*$ni*$ni))/$ni)"
term name = Noni add eqn = "exp( Potential * $Vti)" $Mat
term name = Poni add eqn = "exp( - Potential * $Vti)" $Mat
set eq "Potential * $Vti - log($neq)"
pdbSetString $pdbMat $Sol Equation $eq
} else {
#set a solution variable
set sols [solution list]
if {[lsearch $sols Potential] == -1} {
solution add name = Potential solve damp negative
}
term name = Noni add eqn = "exp( Potential * $Vti)" $Mat
term name = Poni add eqn = "exp( - Potential * $Vti)" $Mat
set eps "([pdbGetString $pdbMat $Sol Permittivityz] * 8.854e-14 / 1.619e-19)"
set eq "$eps * grad(Potential) + $ni * (Poni - Noni) + Charge"
pdbSetString $pdbMat $Sol Equation $eq
}
}
proc PotentialInit { Mat Sol } {
term name = Charge add eqn = 0.0 $Mat
}
APPENDIX B
MODELING THE MOBILITY WITH FLOOPS
The following file, mobilityex.tcl, can be used with FLOOPS to model the mobility in
boron implanted silicon. The user must read in the boron profile and supply the
SIMSdose and hole density (holes).
struct inf=boron1e15.struct
set SIMSdose 5.78e14
set holes 9.5e13
#L is the width of the circumference...
set L 16.0e-8
set IntDose 9.27e14
set LoopDose 8.2e9
set peract [expr $holes/$SIMSdose]
sel z=Boron
set Bdose [FindDose]
sel z=(($SIMSdose/$Bdose)*Boron) name=Boron store
sel z=Boron name=NA
sel z=(NA*$peract) name=NAneg
sel z=(NA-NAneg) name=NN
sel z=Boron name=Int
#atoms/cm2 in plane
set na 1.5e15
set NeutralDose [expr $LoopDose*2.0*3.14159*$L*$na*sqrt($IntDose/($LoopDose*$na*3.14159))]
sel z=NN
set NDose [FindDose]
sel z=(NN*$NeutralDose/$NDose) name=NNL store
#set temperature
set
T
300.0
#/cm3
set pi
3.14
set h
6.625e-34
set hbar [expr "$h / (2.0 * $pi)"]
set kJ
1.38e-23
set k
1.38e-23
153
154
set keV
8.617383e-05
set m0
9.1e-31
set epsilon0
8.854e-12
set epsilons
#g/cm3
set rhos
[expr "11.7 * $epsilon0"]
2.329
set q
1.602e-19
#theta is a function of Temperature see ref[1]
set theta 735.0
#delta for p-type Si in eV
set delta [expr $q*0.044]
#set energy of holes
set
E
"[expr 0.036/($keV*$T)]"
#Model from Sheng S Li Solid State Electronics Vol 21 p1109-1117 1978
set mstarD1
[expr 0.5685*$m0]
set mstarD2
[expr 0.4118*$m0]
set mstarD3
[expr 0.0790*$m0]
set mstarD
[expr 0.7997*$m0]
#from p1111 (m/s)
set us
9.037e3
#D0 (eV/cm)
set D0
[expr 5.7e8*100*$q]
#E1 (eV)
set E1
[expr $q*7.022]
#effective mass in kg
set m0
9.1095e-31
set mstarC1
[expr 0.4484*$m0]
set mstarC2 [expr 0.5231*$m0]
set mstarC3
[expr 0.2517*$m0]
set mstarC
[expr 0.4616*$m0]
#reciprocal relaxation time constant for acoustical phonon scattering
set
taua1 "[expr ([expr 1.414 * pow([expr $q*$E1],2.0)*pow($mstarD1,1.5)*$k * $T ]*
(pow(([expr $q*$E]),0.5))) /[expr ($pi * pow($hbar,4.0) * $rhos * pow($us,2.0))]]"
set
taua2 "[expr ([expr 1.414 * pow([expr $q*$E1],2.0)*pow($mstarD2,1.5)*$k * $T ]*
(pow(([expr $q*$E]),0.5))) /[expr ($pi * pow($hbar,4.0) * $rhos * pow($us,2.0))]]"
set
taua3 "[expr ([expr 1.414 * pow([expr $q*$E1],2.0)*pow($mstarD3,1.5)*$k * $T ]*
(pow(([expr $q*$E]),0.5))) /[expr ($pi * pow($hbar,4.0) * $rhos * pow($us,2.0))]]"
# set
taua2
($us)^2.0)"
"(1.414 * ($E1)^2.0*$mstarD2 * $k * $T * ($E)^0.5) / ($pi * ($hbar)^4.0 * $rhos *
155
# set
taua3
($us)^2.0)"
"(1.414 * ($E1)^2.0*$mstarD3 * $k * $T * ($E)^0.5) / ($pi * ($hbar)^4.0 * $rhos *
#reciprocal relaxation time constant for optical phonon scattering
set
n0
"[expr 1.0/(exp($theta/$T))]"
set x "[expr $E/($keV*$T)]"
set
tauo1 "[expr pow([expr (2.0*$mstarD1)],1.5)*pow($D0,2.0)*(($n0 + 1)*pow(([expr $E$keV*$theta]),0.5)+$n0*[expr pow([expr
$E+$k*$theta],0.5)])/(4.0*$pi*pow($hbar,2.0)*$rhos*$k*$theta)]"
set
tauo2 "[expr pow([expr (2.0*$mstarD2)],1.5)*pow($D0,2.0)*(($n0 + 1)*pow(([expr $E$keV*$theta]),0.5)+$n0*[expr pow([expr
$E+$k*$theta],0.5)])/(4.0*$pi*pow($hbar,2.0)*$rhos*$k*$theta)]"
set
tauo3 "[expr pow([expr (2.0*$mstarD3)],1.5)*pow($D0,2.0)*(($n0 + 1)*pow(([expr $E$keV*$theta]),0.5)+$n0*[expr pow([expr
$E+$k*$theta],0.5)])/(4.0*$pi*pow($hbar,2.0)*$rhos*$k*$theta)]"
#lattice mobility
set
tauL1 "[expr 1.0/(1.0/($taua1)+1.0/($tauo1))]"
set
tauL2 "[expr 1.0/(1.0/($taua2)+1.0/($tauo2))]"
set
tauL3 "[expr 1.0/(1.0/($taua3)+1.0/($tauo3))]"
set
x
"[expr ($E/($keV*$T))]"
set avetauL1 "[expr (4.0/(3.0*pow($pi,0.5)))*$tauL1*pow($x,1.5)*exp(-$x)*$x]"
set avetauL2 "[expr (4.0/(3.0*pow($pi,0.5)))*$tauL2*pow($x,1.5)*exp(-$x)*$x]"
set avetauL3 "[expr (4.0/(3.0*pow($pi,0.5)))*$tauL3*pow($x,1.5)*exp(-$x)*$x]"
set
set
set
muL1
muL2
muL3
"[expr ($q*$avetauL1)/$mstarC1]"
"[expr $q/$mstarC2*$avetauL2]"
"[expr $q/$mstarC3*$avetauL3]"
set
muL
"[expr ($muL1+$muL2*[expr pow(($mstarD2 / $mstarD1),1.5)] + $muL3 * [expr pow
(($mstarD3 / $mstarD1),1.5)]) / [expr (1.0 + pow(($mstarD2 / $mstarD1),1.5) + pow(($mstarD3 /
$mstarD1),1.5))]]"
#ionized impurity scattering mobility (Brooks-Herring formula)
sel z=NAneg name=p
sel z=(p+NAneg*(1-NAneg/NA)) name=pprime
sel z=(pprime*1.0e6)
sel z=((24.0*$pi*$mstarD1*$epsilons*(($k*$T)^2.0))/(($q^2.0)*($h^2)*pprime)) name=b1
sel z=((24.0*$pi*$mstarD2*$epsilons*(($k*$T)^2.0))/(($q^2.0)*($h^2)*pprime)) name=b2
sel z=((24.0*$pi*$mstarD3*$epsilons*(($k*$T)^2.0))/(($q^2.0)*($h^2)*pprime)) name=b3
sel z=(log(b1+1.0)-b1/(b1+1.0)) name=Gatb1
sel z=(log(b2+1.0)-b2/(b2+1.0)) name=Gatb2
sel z=(log(b3+1.0)-b3/(b3+1.0)) name=Gatb3
sel z=NAneg name=NI
156
#convert to meters...
sel z=(NI*1.0e6)
set md 0.01
set md 1.0
sel z=(((2.0^3.5)*($epsilons^2.0)*($mstarD1^0.5)*(($k*$T)^1.5)*$md)/(($pi^1.5)*
($q^3.0)*$mstarC1*NI*Gatb1)) name=muI1
sel z=(((2.0^3.5)*($epsilons^2.0)*($mstarD2^0.5)*(($k*$T)^1.5)*$md)/(($pi^1.5)*
($q^3.0)*$mstarC2*NI*Gatb2)) name=muI2
sel z=(((2.0^3.5)*($epsilons^2.0)*($mstarD3^0.5)*(($k*$T)^1.5)*
$md)/(($pi^1.5)*($q^3.0)*$mstarC3*NI*Gatb3)) name=muI3
sel z=((muI1+muI2*(($mstarD2/$mstarD1)^1.5)+muI3*(($mstarD3/$mstarD1)^1.5))/
(1.0+(($mstarD2/$mstarD1)^1.5)+(($mstarD3/$mstarD1)^1.5))) name=muI
#neutral impurity scattering
set md 0.01
sel z=((2.0*($pi^3.0)*($q^3.0)*($mstarD1^2.0*$md))/(5.0*$epsilons*($h^3.0)*
$mstarC1*NN*1.0e6)) name=muE1
sel z=((2.0*($pi^3.0)*($q^3.0)*($mstarD2^2.0*$md))/(5.0*$epsilons*($h^3.0)*
$mstarC2*NN*1.0e6)) name=muE2
sel z=((2.0*($pi^3.0)*($q^3.0)*($mstarD3^2.0*$md))/(5.0*$epsilons*($h^3.0)*
$mstarC3*NN*1.0e6)) name=muE3
set
EN
"[expr 1.136e-19 * ($mstarD / $m0) * pow(($epsilon0 / $epsilons),2.0)]"
sel z=(muE1*(0.82*((2.0/3.0)*(($k*$T/$EN)^0.5)+(1.0/3.0)*($EN/($k*$T)^0.5)))) name=muN1
sel z=(muE2*(0.82*((2.0/3.0)*(($k*$T/$EN)^0.5)+(1.0/3.0)*($EN/($k*$T)^0.5)))) name=muN2
sel z=(muE3*(0.82*((2.0/3.0)*(($k*$T/$EN)^0.5)+(1.0/3.0)*($EN/($k*$T)^0.5)))) name=muN3
sel z=((muN1+muN2*(($mstarD2/$mstarD1)^1.5)+muN3*(($mstarD3/$mstarD1)^1.5))/
(1.0+(($mstarD2/$mstarD1)^1.5)+(($mstarD3/$mstarD1)^1.5))) name=muN
#neutral loops impurity scattering
sel z=((2.0*($pi^3.0)*($q^3.0)*($mstarD1^2.0*$md))/(5.0*$epsilons*($h^3.0)*
$mstarC1*NNL*1.0e6)) name=muE1L
sel z=((2.0*($pi^3.0)*($q^3.0)*($mstarD2^2.0*$md))/(5.0*$epsilons*($h^3.0)*
$mstarC2*NNL*1.0e6)) name=muE2L
sel z=((2.0*($pi^3.0)*($q^3.0)*($mstarD3^2.0*$md))/(5.0*$epsilons*($h^3.0)*
$mstarC3*NNL*1.0e6)) name=muE3L
set
ENL
"[expr 1.136e-19 * ($mstarD / $m0) * pow(($epsilon0 / $epsilons),2.0)]"
sel z=(muE1L*(0.82*((2.0/3.0)*(($k*$T/$ENL)^0.5)+(1.0/3.0)*($ENL/($k*$T)^0.5)))) name=muN1L
sel z=(muE2L*(0.82*((2.0/3.0)*(($k*$T/$ENL)^0.5)+(1.0/3.0)*($ENL/($k*$T)^0.5)))) name=muN2L
sel z=(muE3L*(0.82*((2.0/3.0)*(($k*$T/$ENL)^0.5)+(1.0/3.0)*($ENL/($k*$T)^0.5)))) name=muN3L
sel z=((muN1L+muN2L*(($mstarD2/$mstarD1)^1.5)+muN3L*(($mstarD3/$mstarD1)^1.5))/
(1.0+(($mstarD2/$mstarD1)^1.5)+(($mstarD3/$mstarD1)^1.5))) name=muNL
sel z=(1.0/(1.0/$muL+1.0/muI)) name=muLI
sel z=(1.0/(1.0/muI+1.0/muN+1.0/muNL)) name=muP
#calculate average mobility
sel z=muP
set lm [layers]
foreach line $lm {
set avemu [lindex $line 2]
157
}
set mob [expr $avemu]
puts "The average mobility is $mob cm2/v-s."
sel z=NAneg
set naneg [FindDose]
#puts "Active dose is $naneg holes/cm2."
puts "The sheet number is $naneg holes/cm2."
set r [expr 1.0/($q*$avemu*$naneg)]
sel z=1.0/($q*$avemu*$naneg) name=resistance
puts "The sheet resistance is $r Ohms/sq."
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(1996).
BIOGRAPHICAL SKETCH
Susan Earles was boron on March 7, 1972, in Rockford, Illinois. She received her
Bachelor of Science degree in May of 1995 and Master of Science degree in May of 1998
from the University of Florida. Since then she has worked toward the Ph.D at the
University of Florida. Her research has focused on the effects of nonmelt laser annealing
on silicon heavily-doped with boron.
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